Free Printable Sequences & Series Test

1.

If $f\left(n\right)=f\left(n-1\right)+7$ and $f\left(1\right)=-18\ \$ then $f\left(5\right)\ =?$

a)

46

b)

-11

c)

11

d)

10

2.

$\ \sum_{i=2}^5\left(i+i^2\right)$ Evaluate.

a)

70

b)

68

c)

108

d)

58

3.

If x >0, and the first 3 terms of a geometric sequence are: 5, x, 45, then which of the following is the value of x?

a)

15

b)

20

c)

25

d)

35

4.

If the pattern shown in the diagrams continues, how many cubes will be contained in the 7th group? (Hint: Find the pattern. It is not necessarily an arithmetic or geometric sequence.)

a)

64

b)

36

c)

49

d)

19

5.

Find the choice that is closest to the sum of a geometric sequence with 15 terms whose first term is 120 and whose common ratio is 0.85.

a)

730

b)

745

c)

820

d)

910

6.

Which of the following represents the series $\frac{2}{9}+\frac{3}{16}+\frac{4}{25}+\frac{5}{36}+\frac{6}{49}?$

a)

$\sum_{n=3}^7\frac{n-1}{n+6}$

b)

$\sum_{n=3}^7\frac{n-1}{n^2+1}$

c)

$\sum_{n=2}^6\frac{n}{\left(n+1\right)^2}$

d)

$\sum_{n=2}^6\frac{n}{n^2+1}$

7.

A sequence is defined by $a_n=a_{n-1}+2a_{n-2}$ with $a_1=-3$ and $a_2=4$ . Which of the following represents the value of $a_6$ ?

a)

-8

b)

14

c)

11

d)

-4

8.

At her job, Pat earns $25,000 for the first year and receives a raise of $1,000 each year. The explicit formula for the $n^{th}$ term of the sequence is $a_n=25,000+\left(n-1\right)1000$ . Which rule best represents the equivalent recursive formula?

a)

$a_n=24,000+1000n$

b)

$a_n=25,000+1000n$

c)

$a_1=25,000\ ;\ a_n=a_{n–1}+1000$

d)

$a_1=25,000;\ a_n=a_{n+1}+1000$

9.

A sequence is defined using the rule $a_n=3a_{n-1}+n$ with $a_1=4$ . Find the value of $a_4-a_3$

a)

45

b)

139

c)

94

d)

184

10.

A geometric sequence is given below. Find the explicit formula for the $n^{th}$ term of this sequence. $10,\ 18,\ 32.4,\ 58.32,\ ...$

a)

$a_n=10\left(1.8\right)^{n–1}$

b)

$a_n=10\left(8\right)^{n–1}$

c)

$a_n=10\left(0.8\right)^{n-1}$

d)

$a_n=8n+2$

11.

Find the sum of the first 25 terms of this sequence:

3, 7, 11, 15,...

a)

1098

b)

1250

c)

1550

d)

1275

12.

The following series is arithmetic: $5+8+11+...+116$
Determine the number of terms in this series. Hint: find n

a)

4

b)

28

c)

36

d)

38

13.

Write the following in simplest form, in terms of x. $\sum_{i=1}^4\left(ix-2i\right)$

a)

$-10x$

b)

$10x-20$

c)

$10x-19$

d)

$10x+12$

14.

A patient is told by his doctor to start a walking program to improve his fitness. The following list shows the amounts (in km) he should walk in each of the first 4 weeks: $1,\ 1.2,\ 1.44,\ 1.728$ If the pattern continues for 20 weeks, how far, to the nearest hundredth of a km, will the patient walk in TOTAL after 20 weeks?

a)

329.48

b)

186.69

c)

253.64

d)

107.36

15.

Here is a list of Luke’s height (in inches) at his last 3 doctor check ups: $54.5,\ 57,\ 59.5$ . Is this trend arithmetic or geometric? And what is the common difference or common ratio?

a)

Arithmetic, d=3.5

b)

Arithmetic, d=1.5

c)

Arithmetic, d=2.5

d)

Geometric, r=2.5

Sequences & Series Test

Total questions: 15

Worksheet time: 4hrs 45mins

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