AnswersDHS Algebra 2 VBase e

Geometric Sequences Answers

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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
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

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)
4

–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
5

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
6

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
7

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
8

A conservationist determines that a particular beach is eroding at a rate of 1.1% each year. When writing an explicit formula to represent the amount of beach remaining each year, which value should she use as the common ratio?

A
0.011
B
0.089
C
0.989
D
1.011
9

On a coordinate plane, 3 points are plotted. The points are (1, 80), (2, 20), (3, 5).

Question illustration
A
f(x) = 80
Option A
B
f(x) = 320
Option B
C
f(x) = 80(4)x – 1
D
f(x) = 320(4)x – 1
10

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
11

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
12

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

Question illustration
A
1
B
2
C
3
D
8
13

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
14

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
15

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
16

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
17

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
18

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
19

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
20

Select two options.

A
The graph will show exponential growth.
B
The graph will appear linear.
C
The domain will be the set of natural numbers.
D
The range will be the set of natural numbers.
E
The graph will show exponential decay.

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