NAME:______________________________________________________
Algebra 2 – Unit 12 Test Review CLASSWORK
DATE:____________
PERIOD:__________
EXPLICIT RULES

The formulas below are given to you on the Reference Sheet. For each formula, identify what each
variable represents and when you would use the formula.
ARITHMETIC SEQUENCE
GEOMETRIC SEQUENCE
GEOMETRIC SERIES
ARITHMETIC AND GEOMETRIC SEQUENCE

For each graph below, identify if it represents an arithmetic or geometric pattern. Then write a
formula to represent the sequence.
PRACTICE WITH ARITHMETIC AND GEOMETRIC SEQUENCE
1. The eighth and tenth terms of a sequence are 64 and 100. If the sequence is either arithmetic or geometric,
the ninth term can not be
1) -82
2) -80
3) 80
4) 82
RECURSIVE SEQUENCE

Each of the following sequences above are recursive. What two things define a recursive
sequence?

Find the first four terms of the following recursive sequences below.
PRACTICE WITH RECURSIVE SEQUENCE
2. Write a recursive formula for each sequence defined below (assume
).
( )
3. Write an explicit formula for
, the nth term of the recursively defined sequences below.
4. Write an explicit formula for
For what values of x would
, the nth term of the recursively defined sequence below.
when
?
5. Find the third term in the recursive sequences
, where
6. Astrid sells art prints through an online retailer. She charges a flat rate per order for an order processing fee,
sales tax, and the same price for each print.
The formula for the cost of buying
buying prints.
prints is given by
. Find a recursive formula for the cost of
7. Mr. Edwards deposits $20,000 into a retirement account that does not earn interest during the first year.
After the first year, the account earns 8% interest at the end of each year.
Write a recursive formula for the balance in the account at the end of each year.