What kind of sequence is this? 4, 24, 144, 864, ... Choices: (A)arithmetic (B)geometric (C)both (D)neither

Identify Given Sequence: Identify the given sequence and list the terms. The given sequence is 4, 24, 144, 864, ...Check Arithmetic Differences: Determine if the sequence is arithmetic by checking if the differences between consecutive terms are equal. Calculate the difference between the second and the first term: 24 - 4 = 20 Calculate the difference between the third and the second term: 144 - 24 = 120 Since 20 is not equal to 120, the differences are not equal. The sequence is not arithmetic.Check Geometric Ratios: Determine if the sequence is geometric by checking if the ratios between consecutive terms are equal. Calculate the ratio of the second term to the first term: 24 / 4 = 6 Calculate the ratio of the third term to the second term: 144 / 24 = 6 Calculate the ratio of the fourth term to the third term: 864 / 144 = 6 Since all ratios are equal to 6, the sequence is geometric.

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What kind of sequence is this? $\newline$ $4, 24, 144, 864, \dots$ $\newline$ Choices: $\newline$ (A) arithmetic $\newline$ (B) geometric $\newline$ (C) both $\newline$ (D) neither

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Math Problems

Algebra 1

Identify arithmetic and geometric sequences

Full solution

Q. What kind of sequence is this?

\newline

4, 24, 144, 864, \dots

\newline

Choices:

\newline

(A) arithmetic

\newline

(B) geometric

\newline

\newline

(D) neither

Identify Given Sequence: Identify the given sequence and list the terms. $\newline$ The given sequence is $4$ , $24$ , $144$ , $864$ , ...
Check Arithmetic Differences: Determine if the sequence is arithmetic by checking if the differences between consecutive terms are equal. $\newline$ Calculate the difference between the second and the first term: $24 - 4 = 20$ $\newline$ Calculate the difference between the third and the second term: $144 - 24 = 120$ $\newline$ Since $20$ is not equal to $120$ , the differences are not equal. $\newline$ The sequence is not arithmetic.
Check Geometric Ratios: Determine if the sequence is geometric by checking if the ratios between consecutive terms are equal. $\newline$ Calculate the ratio of the second term to the first term: $\frac{24}{4} = 6$ $\newline$ Calculate the ratio of the third term to the second term: $\frac{144}{24} = 6$ $\newline$ Calculate the ratio of the fourth term to the third term: $\frac{864}{144} = 6$ $\newline$ Since all ratios are equal to $6$ , the sequence is geometric.