AnswersCA-Mathematics IGeometric Sequences

Geometric Sequences Answers

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1
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Which sequences are geometric? Check all that apply.

A
10, 7.5, 5.625, 4.21875, …
B
160, 40, 10, 2.5, …
C
20, 70, 245, 857.5, …
D
13, 16.5, 20, 23.5, …
E
5, 5.5, 6.05, 6.655, …
F
16, 17.1, 18.2, 19.3, …
2
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3

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Answer:

125

4

The formula f(x + 1) = (f(x)) defines a geometric sequence where f(1) = 18. Which explicit formula can be used to model the same sequence?

Question illustration
A
f(x) = (18)(x – 1)
Option A
B
f (x) = 18 (x minus 1) Superscript two-thirds
Option B
C
f (x) = 18 (two-thirds) Superscript x minus 1
Option C
D
f(x) = (18)x – 1
Option D
5

Which statements are true regarding the sequence below? Check all that apply.It can be represented using the formula f(x + 1) = (f(x)) when f(1) = .It can be represented using the formula .It can be represented using the formula .The domain of the sequence is all real numbers. The range of the sequence is all natural numbers.

Question illustration
A
It can be represented using the formula f(x + 1) = (f(x)) when f(1) = .
Option A
B
It can be represented using the formula .
Option B
C
It can be represented using the formula .
Option C
D
The domain of the sequence is all real numbers.
E
The range of the sequence is all natural numbers.
6

Which statements are true for the given geometric sequence? Check all that apply.

A
The domain is the set of natural numbers.
B
The range is the set of natural numbers.
C
The recursive formula representing the sequence is f(x + 1) = (f(x )) when f(1) = 4.
Option C
D
An explicit formula representing the sequence isf(x) = 4
Option D
E
The sequence shows exponential growth.
7

Which sequence can be generated from the formula f(x + 1) = (f(x))?

Question illustration
A
Option
Option A
B
x, 2x, 4x, 8x, …
Option B
C
Option
Option C
D
x, 2x, 4x, 6x, …
Option D
8

A bouncing ball reaches a height of 54 inches at its first peak, 36 inches at its second peak, and 24 inches at its third peak. Which formula represents this scenario?

A
f(x) = 54
Option A
B
f(x) = 54
Option B
C
f(x) = (54)x
Option C
D
f(x) = (54)x – 1
Option D
9

Shanna writes the formula f(x + 1) = 2.5f(x) when f(1) = 2 to represent this sequence: 2, 5, 12.5, 31.25, …Which error did Shanna make?

A
She used the incorrect common ratio.
B
She used the incorrect initial value.
C
She should have multiplied by f(x) rather then have it as an exponent.
D
She treated the sequence as geometric instead of arithmetic.
10

A sequence has a common ratio of and f(5) = 81. Which explicit formula represents the sequence?

Question illustration
A
f(x) = 24
Option A
B
f(x) = 16
Option B
C
f(x) = 24
Option C
D
f(x) = 16
Option D
11

What is the common ratio for the geometric sequence below, written as a fraction? 768, 480, 300, 187.5, … /

Answers:
Part 1:5
Part 2:8

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