What kind of sequence is this? 89, 178, 356, 712, ... Choices: (A)arithmetic (B)geometric (C)both (D)neither

Check Arithmetic Differences: Let's first check if the sequence is arithmetic by finding the differences between consecutive terms. Given sequence: 89, 178, 356, 712, ... Calculate the differences: 178 - 89, 356 - 178, 712 - 356.Calculate Differences: Perform the calculations: 178 - 89 = 89, 356 - 178 = 178, 712 - 356 = 356. Check if the differences are equal: 89, 178, 356. The differences are not equal, so the sequence is not arithmetic.Check Equal Differences: Now, let's check if the sequence is geometric by finding the ratios between consecutive terms. Given sequence: 89, 178, 356, 712, ... Calculate the ratios: 178 / 89, 356 / 178, 712 / 356.Check Geometric Ratios: Perform the calculations: 178 / 89 = 2, 356 / 178 = 2, 712 / 356 = 2. Check if the ratios are equal: 2, 2, 2. The ratios are equal, so the sequence is geometric.Calculate Ratios: Since the sequence is not arithmetic but has a common ratio, it is a geometric sequence.

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What kind of sequence is this? $\newline$ $89, 178, 356, 712, \dots$ $\newline$ Choices: $\newline$ (A) arithmetic $\newline$ (B) geometric $\newline$ (C) both $\newline$ (D) neither

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Algebra 2

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Q. What kind of sequence is this?

\newline

89, 178, 356, 712, \dots

\newline

Choices:

\newline

(A) arithmetic

\newline

(B) geometric

\newline

\newline

(D) neither

Check Arithmetic Differences: Let's first check if the sequence is arithmetic by finding the differences between consecutive terms. Given sequence: $89, 178, 356, 712, \ldots$ $\newline$ Calculate the differences: $178 - 89, 356 - 178, 712 - 356$ .
Calculate Differences: Perform the calculations: $178 - 89 = 89$ , $356 - 178 = 178$ , $712 - 356 = 356$ . $\newline$ Check if the differences are equal: $89$ , $178$ , $356$ . $\newline$ The differences are not equal, so the sequence is not arithmetic.
Check Equal Differences: Now, let's check if the sequence is geometric by finding the ratios between consecutive terms. Given sequence: $89, 178, 356, 712, \ldots$ $\newline$ Calculate the ratios: $\frac{178}{89}, \frac{356}{178}, \frac{712}{356}.$
Check Geometric Ratios: Perform the calculations: $\frac{178}{89} = 2$ , $\frac{356}{178} = 2$ , $\frac{712}{356} = 2$ . $\newline$ Check if the ratios are equal: $2$ , $2$ , $2$ . $\newline$ The ratios are equal, so the sequence is geometric.
Calculate Ratios: Since the sequence is not arithmetic but has a common ratio, it is a geometric sequence.