Change in Arithmetic &
2.1 Geometric Sequences
Practice Set 1
Problems 1 − 4, determine whether or not the sequence is arithmetic. If it is, find the common
difference.
1. 1,1,2,3,5,8, … 2. −83, −74, −65, −56, …
5 −1 1 1 1 1
3. 4, 2 , 1, ,… 4. , , , ,…
2 4 8 16
2
Problems 5 - 8, write the first five terms of each sequence.
5. 𝑎𝑎𝑛𝑛 = 7 + 5𝑛𝑛 6. 𝑎𝑎𝑛𝑛 = 2𝑛𝑛−1
7. 𝑎𝑎𝑛𝑛 = 120 − 8𝑛𝑛 𝑛𝑛
8. 𝑎𝑎𝑛𝑛 = 𝑛𝑛+2
Problems 9 – 12, find the 28th term of each sequence.
9. 22,25,28,31, … 10. 5,3,1, −1, …
11. 1.7, 1.9, 2.1, 2.3, … 12. 23,16,9,2, …
© 2023 Jean Adams Flamingo Math.com
, Problems 13 − 16, write the general rule for the sequence and find the 14th term.
13. 𝑎𝑎13 = 15, 𝑑𝑑 = 4 14. 𝑎𝑎13 = 15, 𝑑𝑑 = −7
15. 𝑎𝑎15 = 15, 𝑑𝑑 = −11 16. 𝑎𝑎15 = 15, 𝑑𝑑 = 19
Problems 17 − 21, solve.
17. You know your school bus stops at 2-minute intervals. The first stop of the route begins at
6:20 A.M. every day. If your stop is the 18th stop, when will the bus arrive for you?
18. Your grandparents gave you a $500 gift during the holidays, that you deposited in a savings
account. You plan to add $25 to the gift every week to save for summer break, which begins in
June.
A. Write the amount in the account after each deposit as an arithmetic sequence, let 𝑎𝑎1 = 500.
B. If there are 23 weeks before your vacation begins, How much money will you have saved
by summer?
© 2023 Jean Adams Flamingo Math.com
2.1 Geometric Sequences
Practice Set 1
Problems 1 − 4, determine whether or not the sequence is arithmetic. If it is, find the common
difference.
1. 1,1,2,3,5,8, … 2. −83, −74, −65, −56, …
5 −1 1 1 1 1
3. 4, 2 , 1, ,… 4. , , , ,…
2 4 8 16
2
Problems 5 - 8, write the first five terms of each sequence.
5. 𝑎𝑎𝑛𝑛 = 7 + 5𝑛𝑛 6. 𝑎𝑎𝑛𝑛 = 2𝑛𝑛−1
7. 𝑎𝑎𝑛𝑛 = 120 − 8𝑛𝑛 𝑛𝑛
8. 𝑎𝑎𝑛𝑛 = 𝑛𝑛+2
Problems 9 – 12, find the 28th term of each sequence.
9. 22,25,28,31, … 10. 5,3,1, −1, …
11. 1.7, 1.9, 2.1, 2.3, … 12. 23,16,9,2, …
© 2023 Jean Adams Flamingo Math.com
, Problems 13 − 16, write the general rule for the sequence and find the 14th term.
13. 𝑎𝑎13 = 15, 𝑑𝑑 = 4 14. 𝑎𝑎13 = 15, 𝑑𝑑 = −7
15. 𝑎𝑎15 = 15, 𝑑𝑑 = −11 16. 𝑎𝑎15 = 15, 𝑑𝑑 = 19
Problems 17 − 21, solve.
17. You know your school bus stops at 2-minute intervals. The first stop of the route begins at
6:20 A.M. every day. If your stop is the 18th stop, when will the bus arrive for you?
18. Your grandparents gave you a $500 gift during the holidays, that you deposited in a savings
account. You plan to add $25 to the gift every week to save for summer break, which begins in
June.
A. Write the amount in the account after each deposit as an arithmetic sequence, let 𝑎𝑎1 = 500.
B. If there are 23 weeks before your vacation begins, How much money will you have saved
by summer?
© 2023 Jean Adams Flamingo Math.com
