Precalculus
Arithmetic Sequence Practice
Name __________________________
Date _____________ Hour ________
1-2. Given the explicit definition of the arithmetic sequence, find the recursive definition.
1. an  22  5n
2. an  27  2n
3-4. Write both an explicit and recursive formula for the terms in each of the arithmetic sequences
3. 6, 11, 16, 21 . . .
4. 104, 102, 100, 98, …
5-6 Find the explicit formula for the sequences defined recursively below.
5. a1  8, ak 1  ak  7
6. a1  31, ak 1  ak  3
7. A subway pass has a starting value of $100. After one ride, the value of the pass is $98.25. After two
rides, its value is $96.50. After three rides, its value is $94.75. Write an explicit formula to represent the
remaining value of the card as an arithmetic sequence. What is the value of the pass after 15 rides? How
many rides can be taken on the pass?
8. Depreciation is a term used to describe the decrease in value of an item that is owned (an asset). The
depreciated value of an asset is the amount the asset is worth. The table below shows the depreciated value
of a building after each year for the first five years of ownership
Year
Purchase Price
1
2
3
4
5
Depreciated value
300,000
290,000
280,000
270,000
260,000
250,000
Write a formula to describe this arithmetic sequence.
9. You get hired as a diesel mechanic starting at $38,000 per year. You are told at the end of each year
you remain employed you will receive a raise of $1,200. Write an explicit formula for an arithmetic
sequence to describe this scenario.
10. Buses run every 9 minutes starting at 6A.M. You get to the bus stop at 7:16A.M. How long will you
wait for a bus.
11. After one customer buys 4 new tires, a garage recycling bin has 20 tires in it. After another customer
buys 4 new tires, the bin has 24 tires in it. Write an explicit formula to represent the number of tires in the
bin as an arithmetic sequence. How many tires are in the bin after 9 customers buy all new tires/
12. You are given a Regal Cinema gift card valued at $100. After going to see one movie, the balance on
your gift card is $92.50. After you see another movie, the balance on your gift card is $85 . Write an
explicit formula to represent the amount of money left on the card as an arithmetic sequence. What is the
value on your card after 10 movies? How many movies will you be able to see?