Chapter 4 STUDY GUIDE
Sequences
Name: __________________________
Hour: __________________________
1. Consider the sequence shown.
a.
Draw the next two figures of the pattern.
b.
Describe the pattern.
c.
Write a numeric sequence to represent the first 5 figures.
d.
2. Consider the sequence shown.
a.
Draw the next two figures of the pattern.
b.
Write a numeric sequence to represent the first 5 figures.
c.
Describe the sequence using the terms arithmetic sequence, geometric sequence,
common difference, and/or common ratio as they apply.
d.
Write the explicit formula for this sequence.
Chapter 4 STUDY GUIDE
Name: __________________________
Sequences
Hour: __________________________
3. Identify each sequence as arithmetic, geometric, or neither. If the sequence is arithmetic or geometric,
determine the common difference or common ratio.
a.
1, 3, 5, 7, 9, 11
Sequence Type: __________________________
b.
-2, 6, -18, 54, -162
Sequence Type: __________________________
c.
Common Difference/ Ratio: ________________
1, 4, 9, 16, 25
Sequence Type: __________________________
d.
Common Difference/ Ratio: ________________
1 1
1
Common Difference/ Ratio: ________________
1
1, 3 , 9 , 27 , 81
Sequence Type: __________________________
Common Difference/ Ratio: ________________
4. For each sequence, determine whether the sequence is arithmetic or geometric and write an explicit formula.
Using your formula, determine the 12th term in the sequence.
a.
4, 8, 16, 32, 64, 128
Arithmetic or Geometric
Explicit Formula: _______________________
12th term: _____________________________
b.
3
5
7
1, 2 , 2, 2 , 3, 2 , 4
Arithmetic or Geometric
Explicit Formula: _______________________
12th term: _____________________________
c.
-1, -0.25, 0.5, 1.25, 2
Arithmetic or Geometric
Explicit Formula: _______________________
12th term: _____________________________
Chapter 4 STUDY GUIDE
Name: __________________________
Sequences
Hour: __________________________
5. For each sequence, use the recursive formula to determine the next three terms in the sequence. Show your
work.
a.
Let 𝑎1 = 12 and 𝑎𝑛 = 𝑎𝑛−1 + 4
𝑎2 =
𝑎3 =
𝑎4 =
b.
1
1
Let 𝑎1 = 5 and 𝑎𝑛 = 𝑎𝑛−1 (2)
𝑎2 =
𝑎3 =
𝑎4 =
6. Rewrite each explicit formula in simplest form.
a.
𝑎𝑛 = 4 + 3(𝑛 − 1)
b.
𝑎𝑛 = 2 − 5(𝑛 − 1)
6a. ________________________________
6b. _____________________________
7. Marylins’s Bakery made 15 cakes on Monday, 22 cakes on Tuesday, and 29 cakes on Wednesday. If this pattern
continues, how many cakes will Marylin’s Bakery make on Friday?
7. ________________
8. The Johnsons are draining their family swimming pool. After one-half hour, there are 8300 gallons of water in
the pool. After one hour, there are 7900 gallons of water in the pool. After one and one-half hours, there are
7500 gallons of water in the pool. If this pattern continues, how much water will be in the pool after 3 hours?
8. ________________
Chapter 4 STUDY GUIDE
Name: __________________________
Sequences
Hour: __________________________
9. Jesse makes two text messages to his friends to tell them school is cancelled because of storm flooding. Each of
those friends makes two text messages to tell their friends the same news. Each of those friends makes two text
messages to tell their friends the same news, and so on.
a.
Write a numeric sequence to represent the number of text messages made in each of the first 5 sets of
text messages.
b.
Is this an arithmetic or geometric sequence?
9a. ____________________________________
9b. ____________________________________
10. Write the first 4 terms of each sequence.
a.
an arithmetic sequence with a common difference of 6 and a first term of 10
10a. ________________________________________
b.
a geometric sequence with a common ratio of
1
2
and a first term of 48
10b. ________________________________________
c.
an arithmetic sequence with a common difference of 0.25 and a first term of 9
10c. ________________________________________
d.
a geometric sequence with a common ratio of 4 and a first term of 2
10d. ________________________________________
11. Determine the 50th term in the sequence. 𝑎𝑛 = −10 + 4(𝑛 − 1).
11. ___________
12. Determine the 7th term in the sequence.
𝑎𝑛 =
1
3 (3)𝑛−1 .
12. ___________
Chapter 4 STUDY GUIDE
Sequences
Name: __________________________
Hour: __________________________
13. Tell whether each graph represents an arithmetic sequence or a geometric sequence. Explain your reasoning.
a.
b.
__________________________________
__________________________________
__________________________________
__________________________________
___________________________________
___________________________________
___________________________________
___________________________________
____ 14. Which statement describes the pattern shown?
a.
b.
c.
d.
Each figure has 3 fewer squares than the one before it.
Each figure has 6 fewer squares than the one before it.
Each figure has 3 more squares than the one before it.
Each figure has 6 more squares than the one before it.
____ 15. George has agreed to donate $200 to Sun Valley High School for its library. In addition, he will donate $3 for
every book a student at Sun Valley High School reads during the summer. The sequence shown represents the
possible amounts that George will be donating for the summer.
200, 203, 206, 209, 212, 215…
Which explicit formula represents this problem situation?
a.
b.
c.
d.
𝑎𝑛
𝑎𝑛
𝑎𝑛
𝑎𝑛
= 3 + 200(𝑛 − 1)
= 200 + 3(𝑛 − 1)
= 200 + (𝑛 − 3)
= 250 + 3𝑛
Chapter 4 STUDY GUIDE
Sequences
Name: __________________________
Hour: __________________________
____ 16. Which sequence has a common ratio of 4?
a.
b.
c.
d.
9, 5, 1, 3, -7
1, 4, 16, 64, 256
9, 13, 17, 21, 25
1, 4, 16, 64, 256
____ 17. Which represents the explicit formula for the arithmetic sequence 𝑎𝑛 = 12 + 4(𝑛 − 1) in simplest form?
a.
b.
c.
d.
𝑓(𝑛) = 𝑛 + 8
𝑓(𝑛) = 4𝑛 + 12
𝑓(𝑛) = 𝑛 + 16
𝑓(𝑛) = 4𝑛 + 8
____ 18. Which sequence has a common difference of 1.75?
a.
b.
c.
d.
0, 1.75, 3.5, 5.25, -7
0, 1.75, 3.5, 5.25, 7
0, 0.75, 1.5, 2.25, 3
0, 0.75, 1.5, 2.25, -3
____ 19. Determine if the sequence is arithmetic or geometric. Then identify the next term in the sequence.
0.25, 1, 4, 16,…
a.
b.
c.
d.
arithmetic; 32
arithmetic; 64
geometric; 32
geometric; 64
Explicit
Formulas
𝒂𝒏 = 𝒂𝟏 + 𝒅(𝒏 − 𝟏)
𝒂𝒏 = 𝒂𝟏 (𝒓)𝒏−𝟏
Recursive
Formulas
𝒂𝒏 = 𝒂𝒏−𝟏 + 𝒅
𝒂𝒏 = 𝒂𝒏−𝟏 (𝒓)
Chapter 4 STUDY GUIDE
Sequences
Name: __________________________
Hour: __________________________