What kind of sequence is this? 25, 36, 49, 64, ... Choices: (A)arithmetic (B)geometric (C)both (D)neither

Check Differences: Let's first check if the sequence is arithmetic by finding the differences between consecutive terms. Given sequence: 25, 36, 49, 64, ... Calculate the differences: 36 - 25 = 11, 49 - 36 = 13, 64 - 49 = 15. Check if the differences are equal: 11, 13, and 15 are not equal.Check Ratios: Since the differences are not equal, the sequence is not arithmetic. Now, let's check if the sequence is geometric by finding the ratios between consecutive terms. Calculate the ratios: 36 / 25, 49 / 36, 64 / 49. Perform the calculations: 36 / 25 = 1.44, 49 / 36 ≈ 1.3611, 64 / 49 ≈ 1.3061. Check if the ratios are equal: 1.44, 1.3611, and 1.3061 are not equal.Sequence Classification: Since neither the differences nor the ratios between consecutive terms are equal, the sequence is neither arithmetic nor geometric.

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What kind of sequence is this? $\newline$ $25, 36, 49, 64, \dots$ $\newline$ 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

25, 36, 49, 64, \dots

\newline

Choices:

\newline

(A) arithmetic

\newline

(B) geometric

\newline

\newline

(D) neither

Check Differences: Let's first check if the sequence is arithmetic by finding the differences between consecutive terms. Given sequence: $25, 36, 49, 64, \ldots$ $\newline$ Calculate the differences: $36 - 25 = 11$ , $49 - 36 = 13$ , $64 - 49 = 15$ . $\newline$ Check if the differences are equal: $11, 13$ , and $15$ are not equal.
Check Ratios: Since the differences are not equal, the sequence is not arithmetic. Now, let's check if the sequence is geometric by finding the ratios between consecutive terms. $\newline$ Calculate the ratios: $\frac{36}{25}$ , $\frac{49}{36}$ , $\frac{64}{49}$ . $\newline$ Perform the calculations: $\frac{36}{25} = 1.44$ , $\frac{49}{36} \approx 1.3611$ , $\frac{64}{49} \approx 1.3061$ . $\newline$ Check if the ratios are equal: $1.44$ , $1.3611$ , and $1.3061$ are not equal.
Sequence Classification: Since neither the differences nor the ratios between consecutive terms are equal, the sequence is neither arithmetic nor geometric.