What kind of sequence is this? 2, 12, 72, 432, ... Choices: (A)arithmetic (B)geometric (C)both (D)neither

Sequence Type Determination: To determine the type of sequence, we need to examine the relationship between consecutive terms. First, let's check if it's an arithmetic sequence by finding the difference between consecutive terms. Difference between second and first term: 12 - 2 = 10 Difference between third and second term: 72 - 12 = 60 Since the differences are not the same, it is not an arithmetic sequence.Arithmetic Sequence Check: Next, let's check if it's a geometric sequence by finding the ratio between consecutive terms. Ratio of second to first term: 12 / 2 = 6 Ratio of third to second term: 72 / 12 = 6 Ratio of fourth to third term: 432 / 72 = 6 Since the ratios are the same, it is a geometric sequence.Geometric Sequence Check: We can conclude that the sequence is geometric because each term after the first is found by multiplying the previous term by a constant ratio, which in this case is 6.

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What kind of sequence is this? $\newline$ $2, 12, 72, 432, \dots$ $\newline$ Choices: $\newline$ (A) arithmetic $\newline$ (B) geometric $\newline$ (C) both $\newline$ (D) neither

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Math Problems

Grade 8

Identify arithmetic and geometric sequences

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Q. What kind of sequence is this?

\newline

2, 12, 72, 432, \dots

\newline

Choices:

\newline

(A) arithmetic

\newline

(B) geometric

\newline

\newline

(D) neither

Sequence Type Determination: To determine the type of sequence, we need to examine the relationship between consecutive terms. $\newline$ First, let's check if it's an arithmetic sequence by finding the difference between consecutive terms. $\newline$ Difference between second and first term: $12 - 2 = 10$ $\newline$ Difference between third and second term: $72 - 12 = 60$ $\newline$ Since the differences are not the same, it is not an arithmetic sequence.
Arithmetic Sequence Check: Next, let's check if it's a geometric sequence by finding the ratio between consecutive terms. $\newline$ Ratio of second to first term: $\frac{12}{2} = 6$ $\newline$ Ratio of third to second term: $\frac{72}{12} = 6$ $\newline$ Ratio of fourth to third term: $\frac{432}{72} = 6$ $\newline$ Since the ratios are the same, it is a geometric sequence.
Geometric Sequence Check: We can conclude that the sequence is geometric because each term after the first is found by multiplying the previous term by a constant ratio, which in this case is $6$ .