What kind of sequence is this? 61, 74, 87, 100, ... Choices: (A)arithmetic (B)geometric (C)both (D)neither

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What kind of sequence is this?  61, 74, 87, 100, ...    Choices: (A)arithmetic (B)geometric (C)both (D)neither

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Verify Consecutive Differences: Let's verify if the differences between consecutive terms are uniform. Given sequence: 61, 74, 87, 100, ... Are the consecutive differences in the sequence equal? Let's calculate the differences: 74 - 61 = 13, 87 - 74 = 13, 100 - 87 = 13. The consecutive differences in the sequence are equal.Identify Arithmetic Sequence: Since the consecutive differences are equal, this indicates that the sequence is an arithmetic sequence. An arithmetic sequence is defined by having a common difference between consecutive terms. In this case, the common difference is 13.Check for Geometric Sequence: To confirm that this is not a geometric sequence, we need to check if there is a common ratio between consecutive terms. Let's calculate the ratios: 74 / 61 ≈ 1.2131, 87 / 74 ≈ 1.1757, 100 / 87 ≈ 1.1494. The ratios between consecutive terms are not equal, so this is not a geometric sequence.Final Conclusion: Since we have established that the sequence has a common difference and does not have a common ratio, we can conclude that the sequence is an arithmetic sequence and not a geometric sequence. Therefore, the correct choice is (A) arithmetic.

What kind of sequence is this? $\newline$ $61, 74, 87, 100, \dots$ $\newline$ Choices: $\newline$ (A) arithmetic $\newline$ (B) geometric $\newline$ (C) both $\newline$ (D) neither

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What kind of sequence is this?\newline61,74,87,100,…61, 74, 87, 100, \dots61,74,87,100,…\newlineChoices:\newline(A) arithmetic\newline(B) geometric\newline(C) both\newline(D) neither

What kind of sequence is this? $\newline$ $61, 74, 87, 100, \dots$ $\newline$ Choices: $\newline$ (A) arithmetic $\newline$ (B) geometric $\newline$ (C) both $\newline$ (D) neither