Names: __________________________________________________ Date: _____________ Per: ____
11.2- 11.3 Arithmetic and Geometric Sequences Practice
Advanced Algebra 2
Find the missing terms in each sequence. You are given what type of sequence represents each one.
1.
_____, _____, 2, _____, _____, 128 (geometric)
2.
3, _____, _____, 20 (arithmetic)
3.
5, _____, _____, 27 (arithmetic)
4.
32, _____, _____, _____, 162 (geometric)
5.
_____, -10, _____, _____, _____, 14 (arithmetic)
6.
Find the 15th term for the arithmetic sequence –3, 3, 9, …
7.
Find the first 4 terms of the geometric sequence with 𝑎1 = −6 and 𝑟 = − 3
2
Find Sn for each series described. You will need to determine if the series is arithmetic or geometric.
1
8.
160 + 80 + 40 + … , 𝑛 = 6
9.
𝑎1 = 5, 𝑟 = − 2 , 𝑛 = 7
Find the first 3 terms of each arithmetic series.
10.
𝑛 = 14, 𝑎𝑛 = 141, 𝑆𝑛 = 1337
11.
𝑛 = 16, 𝑎𝑛 = 15, 𝑆𝑛 = −120
12. A recovering heart attack patient is told to get on a regular walking program. The patient is told to walk
a distance of 5 km the first week, 8 km the second week, 11 km the third week and so on for a period of
10 weeks. At that point the patient is to maintain the distance walked during the 10th week. How far will
the patient walk during the 10th week?
a. Is the sequence arithmetic or geometric? Write the general term for the sequence.
b. How far will the patient walk during the 10th week? Show all work.
13. A virus reproduces by dividing into two, and after a certain growth period, it divides into two again. As
the virus continues to reproduce, it will continue to divide in two. How many viruses will be in a system
starting with a single virus AFTER 10 divisions?
a. Is the sequence arithmetic or geometric? Write the general term for the sequence.
b. How many viruses will be in a system starting with a single virus AFTER 10 divisions?
14. Sam has purchased a $30,000 car for his business. The car depreciates 30% every year. What will be the
value of the car be after the 5th year? Note: The car is 0 years old when purchased so the first year is the
second entry in the sequence.
a. Is the sequence arithmetic or geometric? Write the general term of the sequence.
b. What will be the value of the car AFTER the 5th year? Show all work.
15. A professional baseball player signs a contract with a beginning salary of $3,000,000 for the first year and
an annual increase of 4% per year beginning in the second year. That is, beginning in year 2, the athlete’s
salary will be 1.04 times what it was in the previous year. What is the athlete’s salary for year 7 of the
contact?
a. Is the sequence arithmetic or geometric? Write the general term of the sequence.
b. What is the athlete’s salary for year 7 of the contract?