Name: __________________________________________________________________
Date: ____________ Period: ____
13.1 Post Test
Problem Learning Target
1–4
13.1: Arithmetic and Geometric Sequences
Score
______ / 20
Percent
______ %
1. Determine whether each sequence is arithmetic or not. If the sequence is arithmetic,
identify the common difference. (5 points)
a. 45, 23, 1, …
Arithmetic:
Yes
No
Common difference:_________
b. -5, -10, -20, -40, …
Arithmetic:
Yes
No
Common difference:_________
Arithmetic:
Yes
No
Common difference:_________
1
2
c. 2, 2 3 , 2 3 , 3, …
2. Determine whether each sequence is geometric or not. If the sequence is geometric,
identify the common ratio. (5 points)
d. 6, 3, 1.5, .75 …
Geometric:
Yes
No
Common ratio:_________
e. 1, 1, 2, 5, …
Geometric:
Yes
No
Common ratio:_________
f.
Geometric:
Yes
No
Common ratio:_________
−5, 20 , −80, 320, …
3. An arithmetic sequence is defined recursively defined as:
a.
𝑎𝑛 = 𝑎𝑛−1 + 7
𝑎1 = −11
Write the first four terms of the sequence. (3 points)
a1  ________, a2  ________, a3  ________, a4  ________, ...
b.
Write the explicit formula for this sequence. (2 points)
an  ________________________
c.
Identify the 25th term for the above sequence. (1 point)
4. Find the first term in the arithmetic sequence: 𝑎3 = 23, 𝑎4 = 19, 𝑎5 = 15, 𝑎6 = 11
o A. 27
o B. 19
o C. 31
o
D. 35
5. Find the explicit formula for this recursively defined geometric sequence:
o
A. 𝑎𝑛 = −4(7)𝑛
o
B. 𝑎𝑛 = 7(−4)𝑛
o
C. 𝑎𝑛 = −4(7)𝑛−1
o
D. 𝑎𝑛 = 7(−4)𝑛−1
𝑎1 = 7
𝑎𝑛 = −4 ∙ 𝑎𝑛−1
6. The following sequence was given to Mr. Awesome’s Algebra classes: 4, 8, 12, 16, … Bob
says this is an arithmetic sequence and Susan says it is geometric. Who is correct and why?
(2 pts)