What kind of sequence is this? 49, 64, 81, 100, ... 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: 49, 64, 81, 100, ... Calculate the differences: 64 - 49 = 15, 81 - 64 = 17, 100 - 81 = 19. The differences between consecutive terms are not constant.Check Geometric Ratios: 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. Calculate the ratios: 64 / 49, 81 / 64, 100 / 81. First ratio: 64 / 49 ≈ 1.306122449, second ratio: 81 / 64 ≈ 1.265625, third ratio: 100 / 81 ≈ 1.234567901. The ratios between consecutive terms are not constant.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? $\newline$ $49, 64, 81, 100, \dots$ $\newline$ 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

49, 64, 81, 100, \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: $49, 64, 81, 100, \ldots$ $\newline$ Calculate the differences: $64 - 49 = 15$ , $81 - 64 = 17$ , $100 - 81 = 19$ . $\newline$ The differences between consecutive terms are not constant.
Check Geometric Ratios: 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. $\newline$ Calculate the ratios: $\frac{64}{49}$ , $\frac{81}{64}$ , $\frac{100}{81}$ . $\newline$ First ratio: $\frac{64}{49} \approx 1.306122449$ , second ratio: $\frac{81}{64} \approx 1.265625$ , third ratio: $\frac{100}{81} \approx 1.234567901$ . $\newline$ The ratios between consecutive terms are not constant.
Sequence Classification: Since the sequence has neither a constant difference nor a constant ratio, it is neither arithmetic nor geometric.