Honors Algebra II/Trig
Chapter 7 Test REVIEW
Name_______________________________
NO CALC
Determine whether the sequence is arithmetic, geometric, or neither. If it is arithmetic,
state the common difference. If it is geometric, state the common ratio.
1. 16, 8, 2, 0.5, 0.125
2. 1, 2, 4, 7, 11
Write a rule for the n-th term of the arithmetic sequence. Then find a15 .
3.  25,29,33,37,41
4. d  5 , a10  60
Write a rule for the n-th term of the arithmetic sequence that has the two given terms.
5. a6  13 , a14  25
Write a rule for the n-th term of the geometric sequence. Then find a 6 .
3 3 12 48
7 7
, , , ,...
6.
7. 35,7, , ,...
28 7 7 7
5 25
Write a rule for the n-th term of the geometric sequence that has the two given terms.
8. a2  2 , a6  512
Write the series using summation notation.
9. 2.8  3.4  4.0  4.6  ...
10.
4 8 12 16
    ...
2 3 4 5
Write a recursive rule for the sequence. The sequence may be arithmetic, geometric, or
neither.
11. 2, 4, 16, 256, 65536
12. 3, 0, -3, 9, 84, 7047
Find the first three iterates of the function for the given initial value.
1
13. f  x   x 2  4 , x0  6
2
Write the following repeating decimal as a fraction in lowest terms.
14. 0.378378378…
Honors Algebra II/Trig
Chapter 7 Test REVIEW
Name_______________________________
CALC
Find the sum of the arithmetic series.
8
15.
 3i  1
9
16.
i 1
 6i  30
i 4
Find the sum of the geometric series.
7
17.
 3 4
i 1
18.
i 1
11
i 1

i 1
1
81 

3
i 1
Find the sum of the infinite geometric series, if it exists.

19.
5
 

i 1  2 
i 1
20.
 2
3  

5
i 1 
Solve the following word problems.
21. A mosquito population in a controlled laboratory condition is estimated to be about 500.
Each day an additional 100 mosquitoes are hatched. The population also declines by 85% every
day from a pesticide and other natural causes. Write a recursive rule for the number a n of
mosquitoes at the start of the n-th day. Find the number of mosquitoes after the 5th day. Describe
what happens to the number of mosquitoes over time.
22. You open a savings account with $500. The account pays 2.2% interest per year,
compounded annually. You do not make any withdrawals from or deposits into the account.
Write a rule for the amount in the account after n years. The find the amount in the account after
10 years.
23. You are stacking soup cans for a display in a grocery store. Your manage wants you to stack
120 cans in layers, with each layer after the first having one less can than the layer before it. One
can should be in the top layer. If you must use all 120 cans, how many cans should be in the first
layer?