What kind of sequence is this? 169, 196, 225, 256, ... Choices: (A)arithmetic (B)geometric (C)both (D)neither

Check Arithmetic Sequence: Let's first check if the sequence is arithmetic by finding the differences between consecutive terms. 169, 196, 225, 256, ... The differences are calculated as follows: 196 - 169 = 27, 225 - 196 = 29, 256 - 225 = 31. The differences between consecutive terms are not constant.Check Geometric Sequence: Since the differences are not constant, the sequence is not arithmetic. Now, let's check if the sequence is geometric by finding the ratios between consecutive terms. The ratios are calculated as follows: 196 / 169, 225 / 196, 256 / 225. We will calculate each ratio to see if they are equal.Calculate Ratios: Calculating the ratios: 196 / 169 ≈ 1.16, 225 / 196 ≈ 1.15, 256 / 225 ≈ 1.14. The ratios between consecutive terms are not equal.Sequence Classification: Since the sequence has neither a constant difference nor a constant ratio, it is neither arithmetic nor geometric.

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What kind of sequence is this? $\newline$ $169, 196, 225, 256, \dots$ $\newline$ Choices: $\newline$ (A) arithmetic $\newline$ (B) geometric $\newline$ (C) both $\newline$ (D) neither

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Algebra 2

Classify formulas and sequences

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Q. What kind of sequence is this?

\newline

169, 196, 225, 256, \dots

\newline

Choices:

\newline

(A) arithmetic

\newline

(B) geometric

\newline

\newline

(D) neither

Check Arithmetic Sequence: Let's first check if the sequence is arithmetic by finding the differences between consecutive terms. $\newline$ $169, 196, 225, 256, \ldots$ $\newline$ The differences are calculated as follows: $\newline$ $196 - 169 = 27$ , $\newline$ $225 - 196 = 29$ , $\newline$ $256 - 225 = 31$ . $\newline$ The differences between consecutive terms are not constant.
Check Geometric Sequence: Since the differences are not constant, the sequence is not arithmetic. Now, let's check if the sequence is geometric by finding the ratios between consecutive terms. $\newline$ The ratios are calculated as follows: $\newline$ $\frac{196}{169}$ , $\newline$ $\frac{225}{196}$ , $\newline$ $\frac{256}{225}$ . $\newline$ We will calculate each ratio to see if they are equal.
Calculate Ratios: Calculating the ratios: $\newline$ $\frac{196}{169} \approx 1.16$ , $\newline$ $\frac{225}{196} \approx 1.15$ , $\newline$ $\frac{256}{225} \approx 1.14$ . $\newline$ The ratios between consecutive terms are not equal.
Sequence Classification: Since the sequence has neither a constant difference nor a constant ratio, it is neither arithmetic nor geometric.