What kind of sequence is this? 4, 20, 100, 500, ... Choices: (A)arithmetic (B)geometric (C)both (D)neither

Check Arithmetic Sequence: Let's check if the sequence is arithmetic by finding the difference between consecutive terms. Difference between second and first term: 20 - 4 = 16 Difference between third and second term: 100 - 20 = 80 Since the differences are not the same, the sequence is not arithmetic.Check Geometric Sequence: Now, let's check if the sequence is geometric by finding the ratio between consecutive terms. Ratio of second to first term: 20 / 4 = 5 Ratio of third to second term: 100 / 20 = 5 Since the ratios are the same, the sequence is geometric.

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What kind of sequence is this? $\newline$ $4, 20, 100, 500, \ldots$ $\newline$ 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

4, 20, 100, 500, \ldots

\newline

Choices:

\newline

(A) arithmetic

\newline

(B) geometric

\newline

\newline

(D) neither

Check Arithmetic Sequence: Let's check if the sequence is arithmetic by finding the difference between consecutive terms. $\newline$ Difference between second and first term: $20 - 4 = 16$ $\newline$ Difference between third and second term: $100 - 20 = 80$ $\newline$ Since the differences are not the same, the sequence is not arithmetic.
Check Geometric Sequence: Now, let's check if the sequence is geometric by finding the ratio between consecutive terms. $\newline$ Ratio of second to first term: $\frac{20}{4} = 5$ $\newline$ Ratio of third to second term: $\frac{100}{20} = 5$ $\newline$ Since the ratios are the same, the sequence is geometric.