What kind of sequence is this? 1, 5, 25, 125, ... Choices: (A)arithmetic (B)geometric (C)both (D)neither

Given Sequence Analysis: Let's look at the given sequence: 1, 5, 25, 125, ... To identify if it's an arithmetic sequence, we need to check if the difference between consecutive terms is constant. Difference between second and first term: 5 - 1 = 4 Difference between third and second term: 25 - 5 = 20 Since the differences are not the same, it is not an arithmetic sequence.Arithmetic Sequence Check: Now, let's check if it's a geometric sequence by finding the ratio between consecutive terms. Ratio of second to first term: 5 / 1 = 5 Ratio of third to second term: 25 / 5 = 5 Ratio of fourth to third term: 125 / 25 = 5 Since the ratios are the same, it is a geometric sequence.

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What kind of sequence is this? $\newline$ $1, 5, 25, 125, \dots$ $\newline$ 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

1, 5, 25, 125, \dots

\newline

Choices:

\newline

(A) arithmetic

\newline

(B) geometric

\newline

\newline

(D) neither

Given Sequence Analysis: Let's look at the given sequence: $1, 5, 25, 125, \ldots$ $\newline$ To identify if it's an arithmetic sequence, we need to check if the difference between consecutive terms is constant. $\newline$ Difference between second and first term: $5 - 1 = 4$ $\newline$ Difference between third and second term: $25 - 5 = 20$ $\newline$ Since the differences are not the same, it is not an arithmetic sequence.
Arithmetic Sequence Check: Now, let's check if it's a geometric sequence by finding the ratio between consecutive terms. $\newline$ Ratio of second to first term: $\frac{5}{1} = 5$ $\newline$ Ratio of third to second term: $\frac{25}{5} = 5$ $\newline$ Ratio of fourth to third term: $\frac{125}{25} = 5$ $\newline$ Since the ratios are the same, it is a geometric sequence.