Free Printable MFCS Recurrence Relations

1.

Select the sequence generated by this recurrence relation

a)

$0,\ \frac{1}{2},\ \frac{2}{5},\ \frac{5}{12},\ ...$

b)

$0,\ \frac{1}{2},\ \frac{5}{2},\ \frac{9}{10},\ ...$

c)

$0,\ 2,\ \frac{1}{4},\ \frac{4}{9},\ ...$

d)

$0,\ \frac{1}{2},\ \frac{1}{5},\ \frac{5}{11},\ ...$

2.

Select the sequence generated by this recurrence relation

a)

3, 7, 11, 15, ...

b)

1, 5, 9, 13, ...

c)

4, 7, 10, 13, ...

d)

7, 11, 15, 19, ...

3.

Select the sequence generated by this recurrence relation

a)

4, 13, 40, 121, ...

b)

2, 7, 22, 67, ...

c)

2, 6, 18, 54, ...

d)

2, 8, 26, 78, ...

4.

Select the sequence generated by this recurrence relation

a)

-2, 1, 7, 17, ...

b)

-2, -1, 1, 7, ...

c)

-2, -9, -23, -51, ...

d)

-2, 1, 7, 19, ...

5.

Select the sequence generated by this recurrence relation

a)

5, 2, 5, 2, ...

b)

5, -2, -9, -16, ...

c)

5, 2, -1, -4, ...

d)

5, 2, -5, -12, ...

6.

Select the sequence generated by this recurrence relation

a)

-1, 6, -14, -46, ...

b)

-1, 14, -46, 194, ...

c)

-1, 7, -9, 23, ...

d)

-1, 14, 46, -194, ...

7.

Select the sequence generated by this recurrence relation

a)

10, 21, 22.1, 22.21, ...

b)

10, 3, 23, 4.3, ...

c)

10, 30, 50, 70, ...

d)

10, 3, 2.3, 2.23, ...

8.

Select the sequence generated by this recurrence relation

a)

$6,\ 1,\ \frac{2}{3},\ \frac{1}{9},\ ...$

b)

$6,\ −1,\ 1\frac{1}{3},\ \frac{5}{9},\ ...$

c)

$6,\ −1,\ \frac{4}{3},\ \frac{4}{9},\ ...$

d)

$6,\ −1,\ \frac{4}{3},\ -\frac{1}{3},\ ...$

9.

Select the sequence generated by this recurrence relation

a)

$0,\ \frac{1}{2},\ \frac{2}{5},\ \frac{5}{12},\ ...$

b)

$0,\ \frac{1}{2},\ \frac{5}{2},\ \frac{9}{10},\ ...$

c)

$0,\ 2,\ \frac{1}{4},\ \frac{4}{9},\ ...$

d)

$0,\ \frac{1}{2},\ \frac{1}{5},\ \frac{5}{11},\ ...$

10.

The first five terms of a sequence are 2, 6, 22, 86, 342.

The recurrence relation that generates this sequence could be:

a)

$P_0=2\ \ \ \ \ \ \ \ \ \ \ \ \ P_{n+1}=P_n\ +\ 4$

b)

$P_0=2\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ P_{n+1}=2P_n\ +\ 2$

c)

$P_0=2\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ P_{n+1}=3P_n$

d)

$P_0=2\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ P_{n+1}=4P_n\ -\ 2$

e)

$P_0=2\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ P_{n+1}=5P_n\ -\ 4$

11.

Identify the common difference of the sequence below:

-2.3, -1.1, 0.1, 1.3,...

a)

-1.2

b)

1.3

c)

1.2

d)

-1.3

12.

Identify the next three terms of the sequence below:

-6, -10, -14,...

a)

-17, -21, -25

b)

17, 21, 25

c)

18, 22, 26

d)

-18, -22, -26

13.

$V_0$ represents:

a)

The starting value

b)

The next term in the sequence

c)

The rule

d)

The current value

14.

$V_{\left(n+1\right)}$ represents:

a)

The starting value

b)

The next term in the sequence

c)

The rule

d)

The current value

15.

$V_n$ represents:

a)

The starting value

b)

The next term in the sequence

c)

The rule

d)

The current value

16.

A recurrence relation is made up of which two parts:

a)

The current value

b)

The starting value

c)

A rule to generate the next term

d)

the next term

17.

The first 3 terms in a sequence, with a starting value of 2 and the rule 'triple and add 2' is:

a)

2, 8, 26

b)

8, 26, 80

c)

2, 6, 20

d)

2, 6, 18

18.

Given the recurrence relation

t_n+1 = 2t_n + 3 and t₃ = 25,

find t₆.

a)

109

b)

206

c)

221

d)

315

e)

445

19.

Given the recurrence relation

t_n+1 = 3t_n + 5 and t₄ = 200,

find the first term.

a)

0

b)

5

c)

14

d)

20

e)

22

20.

Find the recurrence relation that generates the sequence

11, 7, 3, –1, ...

a)

t_n+1 = t_n + 4, where t₁ = 11

b)

t_n+1 = t_n – 4, where t₁ = 11

c)

t_n+1 = –4t_n, where t₁= 11

d)

t_n+1 = 2t_n + 2, where t₁ = 11

e)

t_n+1 = 2t_n – 15, where t1 = 11

21.

A recurrence relation generates the arithmetic sequence

5, 9, 13, 17, ...

Find a rule for the nth term of the sequence.

a)

t_n = n + 4

b)

t_n = 4n – 3

c)

t_n = 4n + 1

d)

t_n = 4n + 5

e)

t_n = 5n + 4

22.

If Ananya is the 8th student in a class and she scored -29 marks in a test, and Aditi is the first student who scored 6 marks, find the recurrence relation that describes the sequence of marks.

a)

t_n+1 = –5t_n, where t₁ = 6

b)

t_n+1 = t_n + 5, where t₁ = 6

c)

t_n+1 = t_n + 13, where t₁ = 6

d)

t_n+1 = t_n – 5, where t₁ = 6

e)

t_n+1 = 7t_n – 11, where t₁ = 6

23.

Write the geometric sequence

10, –30, 90, –270, ...

as a recurrence relation.

a)

t_n+1 = –3t_n, where t₁ = 10

b)

t_n+1 = t_n – 3, where t₁ = 10

c)

t_n+1 = t_n + 10, where t₁ = 10

d)

t_n+1 = –3t_n – 3, where t₁ = 10

e)

t_n+1 = –3t_n + 10, where t₁ = 10

24.

The 5th term in a geometric sequence is 2500 and the common ratio is 5.

Write the recurrence relation that describes this sequence.

a)

t_n+1 = 2t_n, where t₁ = 5

b)

t_n+1 = 4t_n, where t₁ = 5

c)

t_n+1 = 5t_n, where t₁ = 4

d)

t_n+1 = 5t_n + 5, where t₁ = 4

e)

t_n+1 = 5t_n + 4, where t₁ = 5

25.

A recurrence relation generates the arithmetic sequence shown on the graph below.

Find the recurrence relation that generates this set of points.

a)

t_n+1 = 3t_n, where t₁ = –2

b)

t_n+1 = t_n – 3, where t₁ = –2

c)

t_n+1 = t_n + 3, where t₁ = –2

d)

t_n+1 = 2t_n + 5, where t₁ = –2

e)

t_n+1 = 3t_n – 3, where t₁ = –2

26.

A recurrence relation generates the arithmetic sequence shown on the graph below.

Find a rule for the nth term of the sequence.

a)

t_n = n +18

b)

t_n = –3n + 19

c)

t_n = –3n + 22

d)

t_n = –3n + 25

e)

t_n = 19n – 3

27.

Graph the sufficient terms of the sequence

t_n+1 = 1.5t_n – 4 where t₁ = –1.5.

Is it...

a)

a long-term increasing solution

b)

a long-term decreasing solution

c)

a steady-state solution

d)

a different kind of solution

e)

no solution

28.

What value does the sequence defined by

t_n+1 = 0.5t_n + 4, t₁ = 10

take in the long run?

a)

6

b)

-6

c)

7

d)

-7

e)

8

29.

For what value of d does the sequence defined by

t_n+1 = 0.6t_n + d, t₁ = 15

have a long-term steady state solution of 10?

a)

1

b)

-1

c)

3

d)

-3

e)

4

30.

The first five terms of a sequence are 2, 6, 22, 86, 342.

The recurrence relation that generates this sequence could be:

a)

$P_0=2\ \ \ \ \ \ \ \ \ \ \ \ \ P_{n+1}=P_n\ +\ 4$

b)

$P_0=2\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ P_{n+1}=2P_n\ +\ 2$

c)

$P_0=2\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ P_{n+1}=3P_n$

d)

$P_0=2\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ P_{n+1}=4P_n\ -\ 2$

e)

$P_0=2\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ P_{n+1}=5P_n\ -\ 4$

31.

Identify the common difference of the sequence below:

-2.3, -1.1, 0.1, 1.3,...

a)

-1.2

b)

1.3

c)

1.2

d)

-1.3

32.

Identify the next three terms of the sequence below:

-6, -10, -14,...

a)

-17, -21, -25

b)

17, 21, 25

c)

18, 22, 26

d)

-18, -22, -26

33.

$V_0$ represents:

a)

The starting value

b)

The next term in the sequence

c)

The rule

d)

The current value

34.

$V_{\left(n+1\right)}$ represents:

a)

The starting value

b)

The next term in the sequence

c)

The rule

d)

The current value

35.

$V_n$ represents:

a)

The starting value

b)

The next term in the sequence

c)

The rule

d)

The current value

36.

A recurrence relation is made up of which two parts:

a)

The current value

b)

The starting value

c)

A rule to generate the next term

d)

the next term

37.

The first 3 terms in a sequence, with a starting value of 2 and the rule 'triple and add 2' is:

a)

2, 8, 26

b)

8, 26, 80

c)

2, 6, 20

d)

2, 6, 18

38.

Given the recurrence relation

t_n+1 = 2t_n + 3 and t₃ = 25,

find t₆.

a)

109

b)

206

c)

221

d)

315

e)

445

39.

Given the recurrence relation

t_n+1 = 3t_n + 5 and t₄ = 200,

find the first term.

a)

0

b)

5

c)

14

d)

20

e)

22

40.

Find the recurrence relation that generates the sequence

11, 7, 3, –1, ...

a)

t_n+1 = t_n + 4, where t₁ = 11

b)

t_n+1 = t_n – 4, where t₁ = 11

c)

t_n+1 = –4t_n, where t₁= 11

d)

t_n+1 = 2t_n + 2, where t₁ = 11

e)

t_n+1 = 2t_n – 15, where t1 = 11

41.

A recurrence relation generates the arithmetic sequence

5, 9, 13, 17, ...

Find a rule for the nth term of the sequence.

a)

t_n = n + 4

b)

t_n = 4n – 3

c)

t_n = 4n + 1

d)

t_n = 4n + 5

e)

t_n = 5n + 4

42.

If Advait is the 8th student in a class and his test score is -29, and Riyaan is the first student with a score of 6, find the recurrence relation that describes the sequence.

a)

t_n+1 = –5t_n, where t₁ = 6

b)

t_n+1 = t_n + 5, where t₁ = 6

c)

t_n+1 = t_n + 13, where t₁ = 6

d)

t_n+1 = t_n – 5, where t₁ = 6

e)

t_n+1 = 7t_n – 11, where t₁ = 6

43.

Write the geometric sequence

10, –30, 90, –270, ...

as a recurrence relation.

a)

t_n+1 = –3t_n, where t₁ = 10

b)

t_n+1 = t_n – 3, where t₁ = 10

c)

t_n+1 = t_n + 10, where t₁ = 10

d)

t_n+1 = –3t_n – 3, where t₁ = 10

e)

t_n+1 = –3t_n + 10, where t₁ = 10

44.

The 5th term in a geometric sequence is 2500 and the common ratio is 5.

Write the recurrence relation that describes this sequence.

a)

t_n+1 = 2t_n, where t₁ = 5

b)

t_n+1 = 4t_n, where t₁ = 5

c)

t_n+1 = 5t_n, where t₁ = 4

d)

t_n+1 = 5t_n + 5, where t₁ = 4

e)

t_n+1 = 5t_n + 4, where t₁ = 5

45.

A recurrence relation generates the arithmetic sequence shown on the graph below.

Find the recurrence relation that generates this set of points.

a)

t_n+1 = 3t_n, where t₁ = –2

b)

t_n+1 = t_n – 3, where t₁ = –2

c)

t_n+1 = t_n + 3, where t₁ = –2

d)

t_n+1 = 2t_n + 5, where t₁ = –2

e)

t_n+1 = 3t_n – 3, where t₁ = –2

46.

A recurrence relation generates the arithmetic sequence shown on the graph below.

Find a rule for the nth term of the sequence.

a)

t_n = n +18

b)

t_n = –3n + 19

c)

t_n = –3n + 22

d)

t_n = –3n + 25

e)

t_n = 19n – 3

47.

Graph the sufficient terms of the sequence

t_n+1 = 1.5t_n – 4 where t₁ = –1.5.

Is it...

a)

a long-term increasing solution

b)

a long-term decreasing solution

c)

a steady-state solution

d)

a different kind of solution

e)

no solution

48.

What value does the sequence defined by

t_n+1 = 0.5t_n + 4, t₁ = 10

take in the long run?

a)

6

b)

-6

c)

7

d)

-7

e)

8

49.

For what value of d does the sequence defined by

t_n+1 = 0.6t_n + d, t₁ = 15

have a long-term steady state solution of 10?

a)

1

b)

-1

c)

3

d)

-3

e)

4

50.

Let a sequence {a_n} be defined as

a_n= 7 for n = 1

a_n= a_n-1 - 10 for n > 1

Find the formula that represents this sequence in terms of n.

a)

a_n = -10n + 7

b)

a_n = 7n - 10

c)

a_n = 7(-10)^n-1

d)

a_n = -10n + 17

51.

Let a sequence {a_n} be defined as

a_n= -1 for n = 1

a_n= 4*a_n-1 for n > 1

Find the value of a₁₅.

a)

-268,435,456

b)

-1,073,741,824

c)

-60

d)

-16,777,216

52.

Which of the following is a simple statement?

a)

Will it snow today?

b)

8(9+3) = 96

c)

Baseball Season

d)

22 ÷ 11 + 9

53.

Translate the following statement into the correct symbolic statement. "Tracy enjoys Easter, but does not enjoy Thanksgiving."

a)

A ∧ ¬B

b)

¬(A ∧ B)

c)

¬(A ∨ B)

d)

A ∨ ¬B

54.

Consider the statement, "If Kabir practices, he will do better in the math test." Which one of the following statements is false?

a)

Kabir practiced and he did better in the math test.

b)

Kabir practiced, but he did worse in the math test.

c)

Kabir did not practice, but he did better in the math test.

d)

Kabir did not practice and he did worse in the math test.

55.

What is the negation of the statement, "There exists an alien, a, such that a lives on Earth."

a)

There does not exist an alien, a, such that a lives on Earth.

b)

For all aliens, a, in the universe, they do not live on Earth.

c)

For all aliens, a, in the universe, they live on Earth.

d)

There exists an alien, a, such that a does not live on Earth.

56.

Which of the following is logically equivalent to the contrapositive of a statement?

a)

The inverse

b)

The original statement

c)

The converse

d)

No statement is logically equivalent to the contrapositive.

57.

Consider the statement, "If you enjoy watching The Goonies, then you will enjoy Stranger Things." Which statement represents the converse?

a)

If you do not enjoy watching The Goonies, then you will not enjoy Stranger Things.

b)

If you enjoy watching Stranger Things, then you will enjoy watching The Goonies.

c)

If you do not enjoy watching Stranger Things, then you will not enjoy watching The Goonies.

d)

If you enjoy watching The Goonies, then you will not enjoy Stranger Things.

58.

The first five terms of a sequence are 2, 6, 22, 86, 342.

The recurrence relation that generates this sequence could be:

a)

$P_0=2\ \ \ \ \ \ \ \ \ \ \ \ \ P_{n+1}=P_n\ +\ 4$

b)

$P_0=2\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ P_{n+1}=2P_n\ +\ 2$

c)

$P_0=2\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ P_{n+1}=3P_n$

d)

$P_0=2\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ P_{n+1}=4P_n\ -\ 2$

e)

$P_0=2\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ P_{n+1}=5P_n\ -\ 4$

59.

Identify the common difference of the sequence below:

-2.3, -1.1, 0.1, 1.3,...

a)

-1.2

b)

1.3

c)

1.2

d)

-1.3

60.

Identify the next three terms of the sequence below:

-6, -10, -14,...

a)

-17, -21, -25

b)

17, 21, 25

c)

18, 22, 26

d)

-18, -22, -26

61.

$V_0$ represents:

a)

The starting value

b)

The next term in the sequence

c)

The rule

d)

The current value

62.

$V_{\left(n+1\right)}$ represents:

a)

The starting value

b)

The next term in the sequence

c)

The rule

d)

The current value

63.

$V_n$ represents:

a)

The starting value

b)

The next term in the sequence

c)

The rule

d)

The current value

64.

A recurrence relation is made up of which two parts:

a)

The current value

b)

The starting value

c)

A rule to generate the next term

d)

the next term

65.

The first 3 terms in a sequence, with a starting value of 2 and the rule 'triple and add 2' is:

a)

2, 8, 26

b)

8, 26, 80

c)

2, 6, 20

d)

2, 6, 18

66.

Write down the first four terms of the sequence if a₁ = 1 and a_n+1 = 2a_n + 4.

a)

0, 4, 12, 28

b)

1, 4, 10, 18

c)

1, 4, 12, 28

d)

1, 6, 16, 36

e)

6, 16, 34, 72

67.

Given the recurrence relation

t_n+1 = 2t_n + 3 and t₃ = 25,

find t₆.

a)

109

b)

206

c)

221

d)

315

e)

445

68.

Given the recurrence relation

t_n+1 = 3t_n + 5 and t₄ = 200,

find the first term.

a)

0

b)

5

c)

14

d)

20

e)

22

69.

Find the recurrence relation that generates the sequence

11, 7, 3, –1, ...

a)

t_n+1 = t_n + 4, where t₁ = 11

b)

t_n+1 = t_n – 4, where t₁ = 11

c)

t_n+1 = –4t_n, where t₁= 11

d)

t_n+1 = 2t_n + 2, where t₁ = 11

e)

t_n+1 = 2t_n – 15, where t1 = 11

70.

A recurrence relation generates the arithmetic sequence

5, 9, 13, 17, ...

Find a rule for the nth term of the sequence.

a)

t_n = n + 4

b)

t_n = 4n – 3

c)

t_n = 4n + 1

d)

t_n = 4n + 5

e)

t_n = 5n + 4

71.

If Aashi is the 8th student in a class and she scored -29 marks in a test, and Ishaan is the first student who scored 6 marks, find the recurrence relation that describes the sequence of marks.

a)

t_n+1 = –5t_n, where t₁ = 6

b)

t_n+1 = t_n + 5, where t₁ = 6

c)

t_n+1 = t_n + 13, where t₁ = 6

d)

t_n+1 = t_n – 5, where t₁ = 6

e)

t_n+1 = 7t_n – 11, where t₁ = 6

72.

If Naira is the 6th term of an arithmetic progression and Aarush is the 13th term, find the recurrence relation that describes the sequence.

a)

t_n+1 = 4t_n, where t₁ = 2

b)

t_n+1 = t_n + 4, where t₁ = 2

c)

t_n+1 = t_n + 5, where t₁ = 2

d)

t_n+1 = t_n – 4, where t₁= 2

e)

t_n+1 = 3t_n + 2, where t₁ = 2

73.

Write the geometric sequence

10, –30, 90, –270, ...

as a recurrence relation.

a)

t_n+1 = –3t_n, where t₁ = 10

b)

t_n+1 = t_n – 3, where t₁ = 10

c)

t_n+1 = t_n + 10, where t₁ = 10

d)

t_n+1 = –3t_n – 3, where t₁ = 10

e)

t_n+1 = –3t_n + 10, where t₁ = 10

74.

The 5th term in a geometric sequence is 2500 and the common ratio is 5.

Write the recurrence relation that describes this sequence.

a)

t_n+1 = 2t_n, where t₁ = 5

b)

t_n+1 = 4t_n, where t₁ = 5

c)

t_n+1 = 5t_n, where t₁ = 4

d)

t_n+1 = 5t_n + 5, where t₁ = 4

e)

t_n+1 = 5t_n + 4, where t₁ = 5

75.

A recurrence relation generates the arithmetic sequence shown on the graph below.

Find the recurrence relation that generates this set of points.

a)

t_n+1 = 3t_n, where t₁ = –2

b)

t_n+1 = t_n – 3, where t₁ = –2

c)

t_n+1 = t_n + 3, where t₁ = –2

d)

t_n+1 = 2t_n + 5, where t₁ = –2

e)

t_n+1 = 3t_n – 3, where t₁ = –2

76.

A recurrence relation generates the arithmetic sequence shown on the graph below.

Find a rule for the nth term of the sequence.

a)

t_n = n +18

b)

t_n = –3n + 19

c)

t_n = –3n + 22

d)

t_n = –3n + 25

e)

t_n = 19n – 3

77.

Graph the sufficient terms of the sequence

t_n+1 = 1.5t_n – 4 where t₁ = –1.5.

Is it...

a)

a long-term increasing solution

b)

a long-term decreasing solution

c)

a steady-state solution

d)

a different kind of solution

e)

no solution

78.

What value does the sequence defined by

t_n+1 = 0.5t_n + 4, t₁ = 10

take in the long run?

a)

6

b)

-6

c)

7

d)

-7

e)

8

79.

A sequence is defined by

t_n+1 = rt_n + 3 where t₁ = 8.

For what value of r will the sequence have a long-term steady state solution of 6?

a)

0.4

b)

0.5

c)

-0.5

d)

0.6

e)

-0.6

80.

For what value of d does the sequence defined by

t_n+1 = 0.6t_n + d, t₁ = 15

have a long-term steady state solution of 10?

a)

1

b)

-1

c)

3

d)

-3

e)

4

81.

The first five terms of a sequence are 2, 6, 22, 86, 342.

The recurrence relation that generates this sequence could be:

a)

$P_0=2\ \ \ \ \ \ \ \ \ \ \ \ \ P_{n+1}=P_n\ +\ 4$

b)

$P_0=2\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ P_{n+1}=2P_n\ +\ 2$

c)

$P_0=2\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ P_{n+1}=3P_n$

d)

$P_0=2\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ P_{n+1}=4P_n\ -\ 2$

e)

$P_0=2\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ P_{n+1}=5P_n\ -\ 4$

82.

Identify the common difference of the sequence below:

-2.3, -1.1, 0.1, 1.3,...

a)

-1.2

b)

1.3

c)

1.2

d)

-1.3

83.

Identify the next three terms of the sequence below:

-6, -10, -14,...

a)

-17, -21, -25

b)

17, 21, 25

c)

18, 22, 26

d)

-18, -22, -26

84.

$V_0$ represents:

a)

The starting value

b)

The next term in the sequence

c)

The rule

d)

The current value

85.

$V_{\left(n+1\right)}$ represents:

a)

The starting value

b)

The next term in the sequence

c)

The rule

d)

The current value

86.

$V_n$ represents:

a)

The starting value

b)

The next term in the sequence

c)

The rule

d)

The current value

87.

A recurrence relation is made up of which two parts:

a)

The current value

b)

The starting value

c)

A rule to generate the next term

d)

the next term

88.

The first 3 terms in a sequence, with a starting value of 2 and the rule 'triple and add 2' is:

a)

2, 8, 26

b)

8, 26, 80

c)

2, 6, 20

d)

2, 6, 18

89.

Given the recurrence relation

t_n+1 = 2t_n + 3 and t₃ = 25,

find t₆.

a)

109

b)

206

c)

221

d)

315

e)

445

90.

Given the recurrence relation

t_n+1 = 3t_n + 5 and t₄ = 200,

find the first term.

a)

0

b)

5

c)

14

d)

20

e)

22

91.

Find the recurrence relation that generates the sequence

11, 7, 3, –1, ...

a)

t_n+1 = t_n + 4, where t₁ = 11

b)

t_n+1 = t_n – 4, where t₁ = 11

c)

t_n+1 = –4t_n, where t₁= 11

d)

t_n+1 = 2t_n + 2, where t₁ = 11

e)

t_n+1 = 2t_n – 15, where t1 = 11

92.

A recurrence relation generates the arithmetic sequence

5, 9, 13, 17, ...

Find a rule for the nth term of the sequence.

a)

t_n = n + 4

b)

t_n = 4n – 3

c)

t_n = 4n + 1

d)

t_n = 4n + 5

e)

t_n = 5n + 4

93.

If Aarush is the 8th student in a class and his test score is -29, and Aditi is the first student with a score of 6, find the recurrence relation that describes the sequence.

a)

t_n+1 = –5t_n, where t₁ = 6

b)

t_n+1 = t_n + 5, where t₁ = 6

c)

t_n+1 = t_n + 13, where t₁ = 6

d)

t_n+1 = t_n – 5, where t₁ = 6

e)

t_n+1 = 7t_n – 11, where t₁ = 6

94.

Write the geometric sequence

10, –30, 90, –270, ...

as a recurrence relation.

a)

t_n+1 = –3t_n, where t₁ = 10

b)

t_n+1 = t_n – 3, where t₁ = 10

c)

t_n+1 = t_n + 10, where t₁ = 10

d)

t_n+1 = –3t_n – 3, where t₁ = 10

e)

t_n+1 = –3t_n + 10, where t₁ = 10

95.

The 5th term in a geometric sequence is 2500 and the common ratio is 5.

Write the recurrence relation that describes this sequence.

a)

t_n+1 = 2t_n, where t₁ = 5

b)

t_n+1 = 4t_n, where t₁ = 5

c)

t_n+1 = 5t_n, where t₁ = 4

d)

t_n+1 = 5t_n + 5, where t₁ = 4

e)

t_n+1 = 5t_n + 4, where t₁ = 5

96.

A recurrence relation generates the arithmetic sequence shown on the graph below.

Find the recurrence relation that generates this set of points.

a)

t_n+1 = 3t_n, where t₁ = –2

b)

t_n+1 = t_n – 3, where t₁ = –2

c)

t_n+1 = t_n + 3, where t₁ = –2

d)

t_n+1 = 2t_n + 5, where t₁ = –2

e)

t_n+1 = 3t_n – 3, where t₁ = –2

97.

A recurrence relation generates the arithmetic sequence shown on the graph below.

Find a rule for the nth term of the sequence.

a)

t_n = n +18

b)

t_n = –3n + 19

c)

t_n = –3n + 22

d)

t_n = –3n + 25

e)

t_n = 19n – 3

98.

Select the sequence generated by this recurrence relation

a)

3, 7, 11, 15, ...

b)

1, 5, 9, 13, ...

c)

4, 7, 10, 13, ...

d)

7, 11, 15, 19, ...

99.

Select the sequence generated by this recurrence relation

a)

-2, 1, 7, 17, ...

b)

-2, -1, 1, 7, ...

c)

-2, -9, -23, -51, ...

d)

-2, 1, 7, 19, ...

100.

Write down the first four terms of the sequence if a₁ = 1 and a_n+1 = 2a_n + 4.

a)

0, 4, 12, 28

b)

1, 4, 10, 18

c)

1, 4, 12, 28

d)

1, 6, 16, 36

e)

6, 16, 34, 72

101.

Given the recurrence relation

t_n+1 = 2t_n + 3 and t₃ = 25,

find t₆.

a)

109

b)

206

c)

221

d)

315

e)

445

102.

Given the recurrence relation

t_n+1 = 3t_n + 5 and t₄ = 200,

find the first term.

a)

0

b)

5

c)

14

d)

20

e)

22

103.

Find the recurrence relation that generates the sequence

11, 7, 3, –1, ...

a)

t_n+1 = t_n + 4, where t₁ = 11

b)

t_n+1 = t_n – 4, where t₁ = 11

c)

t_n+1 = –4t_n, where t₁= 11

d)

t_n+1 = 2t_n + 2, where t₁ = 11

e)

t_n+1 = 2t_n – 15, where t1 = 11

104.

A recurrence relation generates the arithmetic sequence

5, 9, 13, 17, ...

Find a rule for the nth term of the sequence.

a)

t_n = n + 4

b)

t_n = 4n – 3

c)

t_n = 4n + 1

d)

t_n = 4n + 5

e)

t_n = 5n + 4

105.

If Neha is the 8th student in a class and her test score is -29, and the first student's score is 6, find the recurrence relation that describes the sequence.

a)

t_n+1 = –5t_n, where t₁ = 6

b)

t_n+1 = t_n + 5, where t₁ = 6

c)

t_n+1 = t_n + 13, where t₁ = 6

d)

t_n+1 = t_n – 5, where t₁ = 6

e)

t_n+1 = 7t_n – 11, where t₁ = 6

106.

If Anika is the 6th term of an arithmetic progression and Sanya is the 13th term, find the recurrence relation that describes the sequence.

a)

t_n+1 = 4t_n, where t₁ = 2

b)

t_n+1 = t_n + 4, where t₁ = 2

c)

t_n+1 = t_n + 5, where t₁ = 2

d)

t_n+1 = t_n – 4, where t₁= 2

e)

t_n+1 = 3t_n + 2, where t₁ = 2

107.

Write the geometric sequence

10, –30, 90, –270, ...

as a recurrence relation.

a)

t_n+1 = –3t_n, where t₁ = 10

b)

t_n+1 = t_n – 3, where t₁ = 10

c)

t_n+1 = t_n + 10, where t₁ = 10

d)

t_n+1 = –3t_n – 3, where t₁ = 10

e)

t_n+1 = –3t_n + 10, where t₁ = 10

108.

A recurrence relation generates the arithmetic sequence shown on the graph below.

Find the recurrence relation that generates this set of points.

a)

t_n+1 = 3t_n, where t₁ = –2

b)

t_n+1 = t_n – 3, where t₁ = –2

c)

t_n+1 = t_n + 3, where t₁ = –2

d)

t_n+1 = 2t_n + 5, where t₁ = –2

e)

t_n+1 = 3t_n – 3, where t₁ = –2

109.

A recurrence relation generates the arithmetic sequence shown on the graph below.

Find a rule for the nth term of the sequence.

a)

t_n = n +18

b)

t_n = –3n + 19

c)

t_n = –3n + 22

d)

t_n = –3n + 25

e)

t_n = 19n – 3

110.

Which could be an appropriate rule to model this situation?

a)

Balance = 12 000n + 1.0062

b)

Balance = 12 000 x 1.0062n

c)

Balance = 1 200 x 1.0062ⁿ

d)

Balance = 12 000 x 1.0062ⁿ

111.

What is the value of this loan after 5 months?

a)

$24380.31

b)

$24706.19

c)

$25031.10

d)

$25355.03

e)

$25678.00

112.

The purchase price of a car was $26 000.
Using the reducing balance method, the value of the car is depreciated by 8% each year.
A recurrence relation that can be used to determine the value of the car after n years, $C_n$ is

a)

$C_n\ =\ 26000,\ \ \ \ \ \ \ C_{n+1}\ =\ 0.92C_n$

b)

$C_n\ =\ 26000,\ \ \ \ \ \ \ C_{n+1}\ =\ 1.08C_n$

c)

$C_n\ =\ 26000,\ \ \ \ \ \ \ C_{n+1}\ =\ C_n+8$

d)

$C_n\ =\ 26000,\ \ \ \ \ \ \ C_{n+1}\ =\ C_n-8$

e)

$C_n\ =\ 26000,\ \ \ \ \ \ \ C_{n+1}\ =\ 0.92C_n-8$

113.

Find the balance in the account after the given period.

$12,000 principal earing 4.8% compounded annually after 7 years.

a)

$3,243.19

b)

$16,661.35

c)

$15,243.19

d)

$4,661.35

114.

Find the balance in the account after the given period.

$13,500 deposit earning 3.3% compounded monthly after 1 year

a)

$13,611.38

b)

$14,898.84

c)

$13,537.13

d)

$13, 952.30

115.

Write 0.37 as a percent (%)

a)

37%

b)

.37%

c)

3.7%

116.

Krish borrows $1200 from a bank with 8% simple interest per year. How much will he have to pay back IN TOTAL after 2 years?

a)

$150

b)

$1350

c)

$192

d)

$1392

117.

The amount of payment number 2 that goes towards reducing the principal of the loan is

a)

$486

b)

$502

c)

$504

d)

$996

e)

$998

118.

Identify the next three terms of the sequence below:

-6, -10, -14,...

a)

-17, -21, -25

b)

17, 21, 25

c)

18, 22, 26

d)

-18, -22, -26

119.

The first 3 terms in a sequence, with a starting value of 2 and the rule 'triple and add 2' is:

a)

2, 8, 26

b)

8, 26, 80

c)

2, 6, 20

d)

2, 6, 18

MFCS Recurrence Relations

Total questions: 119

Worksheet time: 6hrs 59mins

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