Algebra 2 Honors
Unit 7
Sequences Quiz Review
1.
Name___________________
Date__January 19 th,2023__
Period__________________
Given the arithmetic sequence 8, 3, −2, −7, …
a. What is the common difference?
b. Write the explicit formula for the sequence.
c. Find the 15𝑡ℎ term of the arithmetic sequence.
2.
If the first term of an arithmetic sequence is 12 and its fifth term is −8, what is the common
difference? Find the 21st term of the sequence using the explicit formula.
3.
What is the 18th term of the arithmetic sequence x+2, 3x+3, 5x+4, …
4.
If the first term of an arithmetic sequence is 10 and its common difference is −4, what term in the
sequence is −50?
5. In an arithmetic sequence, 𝑎5 = 17, 𝑎10 = 57, and the first term of the sequence is 𝑎1 .
a. What is the common difference?
b. Find the first term of the sequence.
c. Write the explicit formula for the sequence.
d. Find the 20𝑡ℎ term of the arithmetic sequence.
6. Manuel Anselmo receives offers from two companies. Company 𝐴 pays $180,000 yearly with a fixed raise
of $4,000 per year. Company 𝐵 pays $200,000 yearly with a fixed raise of $1,500 per year.
a. Write the explicit formula for each sequence representing the companies’ yearly pay after 𝑛 years.
b. Which company pays the greater total amount after 10 years?
7. Given the geometric sequence in which a 1 = 40 and a 2 = 20
a. What is the common ratio?
b. Write the explicit formula.
c. What is the 8th term of the sequence.
3
81
2
8
8. A geometric sequence has a common ratio of and a fourth term of
.
a. What is the first term of the sequence?
b. What is the 9𝑡ℎ term of the sequence?
9. When a golf ball is dropped it has a rebound height that is 87% of the previous height. Write an explicit
and a recursive formula that represents the height of the golf ball if the initial height is 200 centimeters
(cm).
a. Write an explicit and a recursive formula that represents the context.
b. What is the rebound height of the golf ball on the fifth bounce? Round to the nearest hundredth.