What kind of sequence is this? 64, 81, 100, 121, ... Choices: (A)arithmetic (B)geometric (C)both (D)neither

Check Differences: To determine the type of sequence, we first need to check the differences between consecutive terms to see if it is an arithmetic sequence. Let's calculate the differences: 81 - 64 = 17 100 - 81 = 19 121 - 100 = 21Calculate Differences: The differences between consecutive terms are not constant, so the sequence is not arithmetic.Not Arithmetic: Next, we check if it is a geometric sequence by finding the ratios between consecutive terms. Let's calculate the ratios: 81 / 64 = 1.265625 100 / 81 ≈ 1.234567901 121 / 100 = 1.21Check Ratios: The ratios between consecutive terms are not constant, so the sequence is not geometric.Calculate Ratios: Since the sequence is neither arithmetic (constant differences) nor geometric (constant ratios), the correct choice is (D) neither.

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What kind of sequence is this? $\newline$ $64, 81, 100, 121, \dots$ $\newline$ 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

Full solution

Q. What kind of sequence is this?

\newline

64, 81, 100, 121, \dots

\newline

Choices:

\newline

(A) arithmetic

\newline

(B) geometric

\newline

\newline

(D) neither

Check Differences: To determine the type of sequence, we first need to check the differences between consecutive terms to see if it is an arithmetic sequence. $\newline$ Let's calculate the differences: $\newline$ $81 - 64 = 17$ $\newline$ $100 - 81 = 19$ $\newline$ $121 - 100 = 21$
Calculate Differences: The differences between consecutive terms are not constant, so the sequence is not arithmetic.
Not Arithmetic: Next, we check if it is a geometric sequence by finding the ratios between consecutive terms. $\newline$ Let's calculate the ratios: $\newline$ $\frac{81}{64} = 1.265625$ $\newline$ $\frac{100}{81} \approx 1.234567901$ $\newline$ $\frac{121}{100} = 1.21$
Check Ratios: The ratios between consecutive terms are not constant, so the sequence is not geometric.
Calculate Ratios: Since the sequence is neither arithmetic (constant differences) nor geometric (constant ratios), the correct choice is $(D)$ neither.