What kind of sequence is this? 81, 100, 121, 144, ... Choices: (A)arithmetic (B)geometric (C)both (D)neither

Check Differences: Now, let's check if the differences are the same, which is a requirement for an arithmetic sequence. Difference between terms are: 19, 21, and 23. Since the differences are not constant, this is not an arithmetic sequence.Check Ratios: Next, let's check if it's a geometric sequence by finding the ratio between consecutive terms. Ratio between second and first term: 100 / 81 Ratio between third and second term: 121 / 100 Ratio between fourth and third term: 144 / 121Calculate Ratios: Now, let's calculate the ratios to see if they are the same, which is a requirement for a geometric sequence. Ratio between second and first term: 100 / 81 ≈ 1.2346 Ratio between third and second term: 121 / 100 = 1.21 Ratio between fourth and third term: 144 / 121 ≈ 1.1901 Since the ratios are not constant, this is not a geometric sequence.Conclusion: Since the sequence is neither arithmetic (because the differences are not constant) nor geometric (because the ratios are not constant), we can conclude the type of sequence. The sequence is neither arithmetic nor geometric.

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What kind of sequence is this? $\newline$ $81, 100, 121, 144, \dots$ $\newline$ 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

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Q. What kind of sequence is this?

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81, 100, 121, 144, \dots

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Choices:

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(A) arithmetic

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(B) geometric

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\newline

(D) neither

Check Differences: Now, let's check if the differences are the same, which is a requirement for an arithmetic sequence. $\newline$ Difference between terms are: $19$ , $21$ , and $23$ . $\newline$ Since the differences are not constant, this is not an arithmetic sequence.
Check Ratios: Next, let's check if it's a geometric sequence by finding the ratio between consecutive terms. $\newline$ Ratio between second and first term: $\frac{100}{81}$ $\newline$ Ratio between third and second term: $\frac{121}{100}$ $\newline$ Ratio between fourth and third term: $\frac{144}{121}$
Calculate Ratios: Now, let's calculate the ratios to see if they are the same, which is a requirement for a geometric sequence. $\newline$ Ratio between second and first term: $\frac{100}{81} \approx 1.2346$ $\newline$ Ratio between third and second term: $\frac{121}{100} = 1.21$ $\newline$ Ratio between fourth and third term: $\frac{144}{121} \approx 1.1901$ $\newline$ Since the ratios are not constant, this is not a geometric sequence.
Conclusion: Since the sequence is neither arithmetic (because the differences are not constant) nor geometric (because the ratios are not constant), we can conclude the type of sequence. $\newline$ The sequence is neither arithmetic nor geometric.