AnswersCA-Mathematics IGeometric Sequences

Geometric Sequences Answers

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1
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A sequence of numbers begins with 12 and progresses geometrically. Each number is the previous number divided by 2.

A
One-half
Option A
B
2
C
6
D
12
2
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Natalia is writing a recursive formula to represent the sequence.8, 12, 18, 27, ...What value should she use as the common ratio in the formula?

A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
3

Which formula can be used to describe the sequence?, −4, −24, −144,...

Question illustration
A
f(x) = 6
Option A
B
f(x) = −6
Option B
C
f(x) = (6)x − 1
Option C
D
f(x) = (−6)x − 1
Option D
4

Isaak is writing an explicit formula to represent the sequence.64, 112, 196, 343, ...What value should he use as the common ratio in the formula? Write the answer as a decimal rounded to the nearest hundredth.

A
0.75
B
1.75
C
58
D
279
5

The points shown on the graph represent the numbers in a geometric sequence.

Question illustration
A
1
B
2
C
3
D
8
6

–81, 108, –144, 192, ...

A
f(x) = –81
Option A
B
f(x) = –81
Option B
C
f(x) = –81
Option C
D
f(x) = –81
Option D
7

Negative 2 and two-thirds, negative 5 and one-third, negative 10 and two-thirds, negative 21 and one-third, negative 42 and two-thirds, ellipsis

Question illustration
A
f(x + 1) = –2f(x)
B
f(x + 1) = f(x)
Option B
C
f(x + 1) = f(x)
Option C
D
f(x + 1) = 2f(x)
8

Which graph represents a geometric sequence?

A
On a coordinate plane, 5 points are plotted. The points are (1, 1), (2, 3), (3, 5), (4, 7), (5, 9).
Option A
B
On a coordinate plane, 4 points are plotted. The points are (1, 1), (2, 2), (3, 4), (4, 8).
Option B
C
On a coordinate plane, 3 points are plotted. The points are (1, 2), (4, 4), (9, 6).
Option C
D
On a coordinate plane, 3 points are plotted. The points are (1, 1), (2, 4), (3, 9).
Option D
9

Which is the graph of the sequence defined by the function f(x + 1) = f(x) if the initial value of the sequence is 108?

Question illustration
A
Option
B
Option
C
Option
D
Option
10

Pablo generates the function to determine the xth number in a sequence.

Question illustration
A
f(x + 1) = f(x)
Option A
B
f(x) = f(x + 1)
Option B
C
f(x + 1) = f(x)
Option C
D
f(x) = f(x + 1)
Option D
11

A bouncing toy reaches a height of 64 inches at its first peak, 48 inches at its second peak, and 36 inches at its third peak. Which explicit function represents the geometric sequence of the heights of the toy?

A
f(x) = 48
Option A
B
f(x) = 48
Option B
C
f(x) = 64
Option C
D
f(x) = 64
Option D
12

A sequence of numbers begins with 12 and progresses geometrically. Each number is the previous number divided by 2.

A
One-half
Option A
B
2
C
6
D
12
13

Isaak is writing an explicit formula to represent the sequence.64, 112, 196, 343, ...What value should he use as the common ratio in the formula? Write the answer as a decimal rounded to the nearest hundredth.

A
0.75
B
1.75
C
58
D
279
14

Which graph represents a geometric sequence?

A
On a coordinate plane, 5 points are plotted. The points are (1, 1), (2, 3), (3, 5), (4, 7), (5, 9).
Option A
B
On a coordinate plane, 4 points are plotted. The points are (1, 1), (2, 2), (3, 4), (4, 8).
Option B
C
On a coordinate plane, 3 points are plotted. The points are (1, 2), (4, 4), (9, 6).
Option C
D
On a coordinate plane, 3 points are plotted. The points are (1, 1), (2, 4), (3, 9).
Option D
15

–81, 108, –144, 192, ...

A
f(x) = –81
Option A
B
f(x) = –81
Option B
C
f(x) = –81
Option C
D
f(x) = –81
Option D
16

Natalia is writing a recursive formula to represent the sequence.8, 12, 18, 27, ...What value should she use as the common ratio in the formula?

A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
17

Sebastian writes the recursive formula f(x+1) = 4f(x) to represent a geometric sequence whose second term is 12.

A
f(x) = 12(4)x
B
f(x) = 3(4)x − 1
C
f(x) = 4(12)x
D
f(x) = 4(3)x − 1
18

The points shown on the graph represent the numbers in a geometric sequence.

Question illustration
A
1
B
2
C
3
D
8
19

Lena is asked to write an explicit formula for the graphed geometric sequence.

Question illustration
A
1.0
B
1.5
C
2.5
D
2.0
20

Which is the graph of the sequence defined by the function f(x + 1) = f(x) if the initial value of the sequence is 108?

Question illustration
A
Option
B
Option
C
Option
D
Option

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