Name:
Secondary Math I – Chapter 4 Test Review
Date:
Period:
1. Identify each sequence as arithmetic or geometric. Then determine the common difference or common ratio for
each sequence.
a. 2, 5, 8, 11, 14, 17
b. −6, 12, −24, 48, −96
12
arithmetic; 𝑑 = 5 − 2 = 3
geometric; 𝑟 = −6 = −2
c. 1, ,
1 1 1
1
, ,
4 16 64 256
1
geometric; 𝑟 = 4
d. 0.13, 0.38, 0.63, 0.88, 1.13
arithmetic; 𝑑 = .38 − .13 = .25
2. Write a recursive formula for each sequence and then
determine the unknown term.
a. 0.15, 0.17, 0.19, 0.21, _______
𝑎1 = 0.15; 𝑎𝑛 = 𝑎𝑛−1 + 0.02; 0.23
3. Shelby’s printer had 500 sheets of paper in it. After
Monday, there were 466 sheets of paper. After Tuesday,
there were 432 sheets of paper. After Wednesday, there
were 398 sheets of paper. If this pattern continues, how
many sheets of paper will be left after Friday?
330 sheets of paper
1 1 1
1
, , , _______,
6 12 24
96
1
1 1
𝑔1 = 6; 𝑔𝑛 = 𝑔𝑛−1 ∙ 2; 48
b.
4. Consider the sequence shown. Describe the pattern and draw the next three figures of the pattern.
Each Step rotates the arrow by 135 degrees, or 3/8th of a rotation
5. Raymond is filling his kitchen sink to wash dishes. After one minute, there are 2.75 gallons of water in the sink.
After two minutes, there are 5.5 gallons of water in the sink. After three minutes, there are 8.25 gallons of water in
the sink. If this pattern continues, how many gallons of water will be in the sink after five minutes?
13.75 gallons
6. Brittany is a scientist. She is recording the number of
cells in a dish. After each hour, the cell divides into four
cells. The sequence shown represents the growth of the
cells.
1, 4, 16, 64, 256
Write an explicit formula to represent this situation.
𝑔𝑛 = 1(4)𝑛−1
7. Determine the 73rd term for the geometric sequence
defined by the formula 𝑔𝑛 = 12 ∙ 3𝑛−1 .
2.703 × 1035
9. Graph the ordered pairs for the sequence given by the
10. Write a sequence with 7 terms, starting with 6 and a
common difference of -2.5.
6, 3.5, 1, −1.5, −4, −6.5, −9
formula 𝑔𝑛 = 32 ∙
1 𝑛−1
(2) .
8. Determine the 10th term of the arithmetic sequence
1
defined by the formula 𝑎𝑛 = 1 + 3 (𝑛 − 1).
4
11. Write a sequence with 5 terms, starting with 5, and a
common ratio of 4.
5, 20, 80, 320, 1280
12. Consider the sequence shown. Draw the next two figures of the pattern.
a. Describe the sequence.
It starts with four tiles in a square and then adds 2 tiles to
each corner the next step, duplicating the original square
in each corner in two steps and then adding 2 to each
corner, …
b. Write a numeric sequence to represent the first 6
figures.
4, 12, 20, 28, 36, 44
c. Write an explicit formula for this sequence.
𝑎𝑛 = 4 + 8(𝑛 − 1)
d. Write a recursive formula for this sequence.
𝑎1 = 4; 𝑎𝑛 = 𝑎𝑛−1 + 8
e. Determine the number of squares in the 25th figure in
the pattern.
196
f. Determine the number of squares in the 87th figure in
the pattern.
692
13. Write an explicit formula for each sequence and then
determine the unknown term.
14. Graph the ordered pairs for the sequence given by
the formula 𝑎𝑛 = 2 + 4(𝑛 − 1)
9 9
4 8
1 𝑛−1 9
(2) ; 2
a. 18, 9, _______ , ,
𝑔𝑛 = 18 ∙
b. 19, 12, 5, −2, _______
𝑓(𝑛) = 19 − 7(𝑛 − 1); −9
or
𝑓(𝑛) = −7𝑛 + 26
15. Which sequence has a common ratio of -3?
16. Which represents the explicit formula for the
arithmetic sequence 𝑎𝑛 = 12 + 3(𝑛 − 1) in function
form?
a. 9, 6, 3, 0, −3
a. 𝑓(𝑛) = 9𝑛 − 3
b. 1, 3, 9, 27, 81
b. 𝑓(𝑛) = 3𝑛 + 15
c. 9, 12, 15, 18, 21
c. 𝑓(𝑛) = 3𝑛 + 9
d. 1, −3, 9, −27, 81
d. 𝑓(𝑛) = 3𝑛 − 11