Name:____________________________
Sequences: Mixed Practice
Date:___________________
Algebra I Common Core
1. What is the difference between an arithmetic and a
geometric sequence?
2. Identify whether the graph represents a geometric
or arithmetic sequence. Explain.
3. Identify whether the graph represents a geometric
or arithmetic sequence. Explain.
4. What is the eight term of this sequence?
𝑎𝑛 = 3𝑛 + 4
5. What is the ninth term of this sequence?
𝑎𝑛 = (−1)𝑛−1 ∙ 𝑛2
6. What is the seventh term of this sequence?
1 𝑛−1
𝑎𝑛 = 12 ( )
2
7. What is the common difference of the arithmetic
sequence
?
8. What is the common ratio of the geometric
sequence shown below?
1)
1)
2)
2) 2
3) 3
3)
4) 9
4)
9. Given the sequence: {10,2, −6, −14, … }
a) Write an explicit formula for this sequence.
b) Write a recursive formula for this sequence.
1 1 1
1
10. Given the sequence: {1, 2 , 4 , 8 , 16 , … }
a) Write an explicit formula for this sequence.
b) Write a recursive formula for this sequence.
11. A sequence has the following terms:
,
,
,
. Which formula represents
the nth term in the sequence?
12. Identify each sequence as arithmetic or
geometric. Explain your answer, and write an
explicit formula for the sequence.
1)
a) 7, 16, 25, 34, …
2)
3)
4)
b) 36, 12, 4, …
13. Write the first 5 terms of the sequence described
below with recursive equations:
14. What is the seventh term of this sequence?
𝑎1 = 3
𝑎𝑛 = 𝑎𝑛−1 + 6
𝑎1 = 5
𝑎𝑛 = 𝑎𝑛−1 − 4
1) 9
2) 27
3) 60
4) 39
15. Find 𝑎12 for -17, -13, -9, …
16. Find 𝑎8 for 4, -12, 36, …
17. Find the third term in the recursive sequence
, where
.
18. What are the first four terms of this sequence?
𝑓(1) = −2; 𝑓(𝑛) = 𝑓(𝑛 − 1) + 5
19. Find the common difference (d) in the arithmetic
sequence whose 1st term is 4 and whose 11th term is
64.
20. In an arithmetic sequence,
Determine a formula for
sequence.
, the
and
term of this
.
21. Erin is traveling abroad this summer and would like to have a bit of spending cash while she’s overseas.
She has 100 dollars already saved and she plans on saving 40 dollars a month.
c) Graph this sequence for 1 m  5.
a) Fill out the table below for the amount of money she saves
as a function of how many months she has been saving.
b) Give a recursive definition for the sequence 𝑎(𝑚).
[*Reminder: Don’t forget to give an initial value.]
22. Edna is building a tower out of paper cups. In each row (counting from the floor up), there are two less
cups than the row below it. The first row has 26 cups in it.
a) State the number of cups in the second, third,
and fourth rows.
b) Give a recursive definition for this
arithmetic sequence.
c) How many cups will be in the 11th row? Show the calculation that leads to your answer.
Lesson Summary:




How do we determine if a sequence is arithmetic or geometric?
How can we write an explicit formula to find the nth term?
How do we graph and find the nth term of an explicit formula?
How do we find terms in a recursive formula?