Practice with
Arithmetic and Geometric Sequences and Series

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Solve the following problems dealing with Arithmetic and Geometric Sequences and Series.
Look carefully at each question to determine with "which" sequence you are working. 
You may wish to have your graphing calculator handy. 

 

1.

Find the sum of the first 20 terms of the sequence 4, 6, 8, 10, ...
 

Answer 

 

 

2.

 Find the sum of the sequence
-8, -5, -2, ..., 7

Answer 

 

 

3.

Find the 9th term of the sequence

 Answer 

 

 

4.

Evaluate this series using a formula:

 

Answer 

 

 

5.

Insert three geometric means
between 1 and 81.

 

Answer 

 

 

6.

Find a6 for an arithmetic sequence where a1 = 3x+1 and d = 2x+6.

 

Answer 

 

 

7.

Find t12 for a geometric sequence
where   t1 = 2 + 2i   and   r = 3.

 

Answer 

 

 

8.

 A display of cans on a grocery shelf consists of 20 cans on the bottom, 18 cans in the next row, and so on in an arithmetic sequence, until the top row has 4 cans.  How many cans, in total, are in the display?

Answer 

 

 

9.

How many terms of the arithmetic sequence -3, 2, 7, ... must be added together for the sum of the series to be 116?

Answer 

 


 

10.

Find the indicated sum

Answer 

 

 

11.

Given the sequence -4, 0, 4, 8, 12, ..., Darius devises a formula for the sum of n terms of the sequence.  His formula is

Is this formula correct?  Show work to support your answer.

Answer 

 

 

12.

pic

Which of the following choices is the formula
for the nth term of the sequence
54, 18, 6, ... ?

Choose:

m12a                 m12b
m12c                m12d

 


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