Free Printable Arithmetic and Geometric Series

1.

What is the sum of the following infinite geometric series?
$3+\frac{6}{5}+\frac{12}{25}+\frac{24}{125}+.....$

a)

$\frac{609}{125}$

b)

5

c)

$\frac{15}{2}$

d)

$\frac{6}{5}$

2.

At the beginning of the school year, Math Lab had 745 students attend for the week. Each week that followed, the number of students attending decreased by 10%. Approximately how many total visits were there to Math Lab in the first nine weeks?

a)

828

b)

6035

c)

671

d)

4563

3.

What is the sum of the following series?
$\sum_{k=1}^{31}\left(\frac{3}{4}-7\right)$

a)

496

b)

$143\ \frac{3}{8}$

c)

$145\ \frac{5}{8}$

d)

155

4.

Evaluate the series below.
$\sum_{k=0}^{\infty}\frac{2}{3}\left(\frac{1}{\left(8\right)}\right)^k$

a)

$\frac{3}{8}$

b)

$\frac{8}{3}$

c)

$\frac{16}{21}$

d)

$\frac{21}{16}$

5.

Julia is saving up for an iphone 11 Pro Max. She can put away $30 this week. Each week after that she can increase the amount she puts away per week by $5. How much will she have saved in 12 weeks?

a)

$870

b)

$1080

c)

$720

d)

$950

6.

What is the sum of the following series?

632 + 615 + 598 + .... 326

a)

1916

b)

3066

c)

8622

d)

9101

7.

What is the sum of the first 6 terms in the series?

7 + (-21) + 63 + ....

a)

-15305

b)

15305

c)

3829

d)

-3829

8.

Write the following series in sigma notation for the first 6 terms.

a)

$\sum_{k=1}^6-81\left(-\frac{2}{3}\right)^k$

b)

$\sum_{k=1}^5-81\left(-\frac{2}{3}\right)^{\left(k-1\right)}$

c)

$\sum_{k=0}^6-81\left(-\frac{2}{3}\right)^k$

d)

$\sum_{k=0}^5-81\left(-\frac{2}{3}\right)^k$

9.

What is the proper expansion for the following series?
$\sum_{k=0}^33\left(-2\right)^k$

a)

3 + (-6) + 18

b)

3 + (-6) +12

c)

3 + (-6) + 12 + (-24)

d)

-6 + 12 + (-24) + 48

10.

What is the sum of the series below?
$\sum_{k=1}^{\infty}6\left(-2\right)^{\left(k-1\right)}$

a)

2

b)

-12

c)

105,400

d)

No sum exists

Arithmetic and Geometric Series

Total questions: 10

Worksheet time: 31mins

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