What kind of sequence is this? 121, 144, 169, 196, ... Choices: (A)arithmetic (B)geometric (C)both (D)neither

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What kind of sequence is this?  121, 144, 169, 196, ...    Choices: (A)arithmetic (B)geometric (C)both (D)neither

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Verify Differences Uniform: Let's verify if the differences between consecutive terms are uniform. Given sequence: 121, 144, 169, 196, ... Are the consecutive differences in the sequence equal? 144 - 121 = 23, 169 - 144 = 25, 196 - 169 = 27. The consecutive differences in the sequence are not equal, but they are increasing by 2 each time.Check Ratios Equal: Let's check whether the ratios between consecutive terms are equal. Given sequence: 121, 144, 169, 196, ... Are the ratios between consecutive terms in the sequence equal? 144 / 121 is not an integer, 169 / 144 is not an integer, 196 / 169 is not an integer. The sequence does not have a common ratio.Identify Sequence Type: Arithmetic sequence: Consecutive terms have a common difference. Geometric sequence: Consecutive terms have a common ratio. 121, 144, 169, 196, ... What type of sequence is this? The sequence has increasing differences and no common ratio. However, the differences are increasing by a constant amount, which suggests a pattern. Let's examine the numbers more closely. These numbers are perfect squares: 121 = 11^2, 144 = 12^2, 169 = 13^2, 196 = 14^2. Each term is the square of consecutive integers, which means the difference between consecutive terms will always be an odd number that increases by 2 each time. This is a special characteristic of perfect squares.Determine Correct Choice: Since the sequence is neither arithmetic (no common difference) nor geometric (no common ratio), but it does follow a specific pattern of perfect squares of consecutive integers, the correct choice is neither arithmetic nor geometric.

What kind of sequence is this? $\newline$ $121, 144, 169, 196, \dots$ $\newline$ Choices: $\newline$ (A) arithmetic $\newline$ (B) geometric $\newline$ (C) both $\newline$ (D) neither

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What kind of sequence is this?\newline121,144,169,196,…121, 144, 169, 196, \dots121,144,169,196,…\newlineChoices:\newline(A) arithmetic\newline(B) geometric\newline(C) both\newline(D) neither

What kind of sequence is this? $\newline$ $121, 144, 169, 196, \dots$ $\newline$ Choices: $\newline$ (A) arithmetic $\newline$ (B) geometric $\newline$ (C) both $\newline$ (D) neither