What kind of sequence is this? 1, 4, 9, 16, ... Choices: (A)arithmetic (B)geometric (C)both (D)neither

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What kind of sequence is this?  1, 4, 9, 16, ...    Choices: (A)arithmetic (B)geometric (C)both (D)neither

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Examine Number Pattern: To determine the type of sequence, we need to examine the pattern of the numbers given in the sequence: 1, 4, 9, 16, ... First, let's check if it's an arithmetic sequence. An arithmetic sequence has a common difference between consecutive terms. We calculate the difference between the second and the first term: 4 - 1 = 3. Then, we calculate the difference between the third and the second term: 9 - 4 = 5. Since the differences are not the same, it is not an arithmetic sequence.Check Arithmetic Sequence: Next, let's check if it's a geometric sequence. A geometric sequence has a common ratio between consecutive terms. We calculate the ratio between the second and the first term: 4 / 1 = 4. Then, we calculate the ratio between the third and the second term: 9 / 4. Since 9 is not a multiple of 4, the ratio is not consistent, and therefore, it is not a geometric sequence.Check Geometric Sequence: Since the sequence is neither arithmetic nor geometric, let's consider other patterns. We notice that each term is a square of an integer: 1^2, 2^2, 3^2, 4^2, ... This pattern is characteristic of a sequence of perfect squares, which is neither arithmetic nor geometric.

What kind of sequence is this? $\newline$ $1, 4, 9, 16, \dots$ $\newline$ Choices: $\newline$ (A) arithmetic $\newline$ (B) geometric $\newline$ (C) both $\newline$ (D) neither

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What kind of sequence is this?\newline1,4,9,16,…1, 4, 9, 16, \dots1,4,9,16,…\newlineChoices:\newline(A) arithmetic\newline(B) geometric\newline(C) both\newline(D) neither

What kind of sequence is this? $\newline$ $1, 4, 9, 16, \dots$ $\newline$ Choices: $\newline$ (A) arithmetic $\newline$ (B) geometric $\newline$ (C) both $\newline$ (D) neither