Free Printable Recurrence Relations

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Recurrence Relations

Total questions: 15

Worksheet time: 1hrs 15mins

Name

Class

Date

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

0, 4, 12, 28

1, 4, 10, 18

1, 4, 12, 28

1, 6, 16, 36

6, 16, 34, 72

Given the recurrence relation

t_n+1 = 2t_n + 3 and t₃ = 25,

find t₆.

109

206

221

315

445

Given the recurrence relation

t_n+1 = 3t_n + 5 and t₄ = 200,

find the first term.

Find the recurrence relation that generates the sequence

11, 7, 3, –1, ...

t_n+1 = t_n + 4, where t₁ = 11

t_n+1 = t_n – 4, where t₁ = 11

t_n+1 = –4t_n, where t₁= 11

t_n+1 = 2t_n + 2, where t₁ = 11

t_n+1 = 2t_n – 15, where t1 = 11

A recurrence relation generates the arithmetic sequence

5, 9, 13, 17, ...

Find a rule for the nth term of the sequence.

t_n = n + 4

t_n = 4n – 3

t_n = 4n + 1

t_n = 4n + 5

t_n = 5n + 4

If the 8th term of an arithmetic progression is –29, and the first term is 6, find the recurrence relation that describes the sequence.

t_n+1 = –5t_n, where t₁ = 6

t_n+1 = t_n + 5, where t₁ = 6

t_n+1 = t_n + 13, where t₁ = 6

t_n+1 = t_n – 5, where t₁ = 6

t_n+1 = 7t_n – 11, where t₁ = 6

If the 6thterm of an arithmetic progression is 22,

and the 13th term is 50,

find the recurrence relation that describes the sequence.

t_n+1 = 4t_n, where t₁ = 2

t_n+1 = t_n + 4, where t₁ = 2

t_n+1 = t_n + 5, where t₁ = 2

t_n+1 = t_n – 4, where t₁= 2

t_n+1 = 3t_n + 2, where t₁ = 2

Write the geometric sequence

10, –30, 90, –270, ...

as a recurrence relation.

t_n+1 = –3t_n, where t₁ = 10

t_n+1 = t_n – 3, where t₁ = 10

t_n+1 = t_n + 10, where t₁ = 10

t_n+1 = –3t_n – 3, where t₁ = 10

t_n+1 = –3t_n + 10, where t₁ = 10

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

Write the recurrence relation that describes this sequence.

t_n+1 = 2t_n, where t₁ = 5

t_n+1 = 4t_n, where t₁ = 5

t_n+1 = 5t_n, where t₁ = 4

t_n+1 = 5t_n + 5, where t₁ = 4

t_n+1 = 5t_n + 4, where t₁ = 5

10.

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

Find the recurrence relation that generates this set of points.

t_n+1 = 3t_n, where t₁ = –2

t_n+1 = t_n – 3, where t₁ = –2

t_n+1 = t_n + 3, where t₁ = –2

t_n+1 = 2t_n + 5, where t₁ = –2

t_n+1 = 3t_n – 3, where t₁ = –2

11.

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

Find a rule for the nth term of the sequence.

t_n = n +18

t_n = –3n + 19

t_n = –3n + 22

t_n = –3n + 25

t_n = 19n – 3

12.

Graph the sufficient terms of the sequence

t_n+1 = 1.5t_n – 4 where t₁ = –1.5.

Is it...

a long-term increasing solution

a long-term decreasing solution

a steady-state solution

a different kind of solution

no solution

13.

What value does the sequence defined by

t_n+1 = 0.5t_n + 4, t₁ = 10

take in the long run?

-6

-7

14.

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?

0.4

0.5

-0.5

0.6

-0.6

15.

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?

-1

-3

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Recurrence Relations

Total questions: 15

Worksheet time: 1hrs 15mins

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