What kind of sequence is this? $\newline$ $958, 958, 958, 958, \ldots$ $\newline$ Choices: $\newline$ (A) arithmetic $\newline$ (B) geometric $\newline$ (C) both $\newline$ (D) neither

Full solution

Q. What kind of sequence is this?

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958, 958, 958, 958, \ldots

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Choices:

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(A) arithmetic

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(B) geometric

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(D) neither

Arithmetic Sequence Check: An arithmetic sequence is a sequence of numbers in which each term after the first is obtained by adding a constant difference to the previous term. To determine if this is an arithmetic sequence, we need to check if the difference between consecutive terms is constant.
Constant Difference Calculation: The difference between the first and second term is $958 - 958 = 0$ . Similarly, the difference between the second and third term is also $958 - 958 = 0$ . Since the difference is constant, this sequence can be considered an arithmetic sequence with a common difference of $0$ .
Geometric Sequence Check: A geometric sequence is a sequence of numbers where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the ratio. To determine if this is a geometric sequence, we need to check if the ratio between consecutive terms is constant.
Constant Ratio Calculation: The ratio between the first and second term is $958 / 958 = 1$ . Similarly, the ratio between the second and third term is also $958 / 958 = 1$ . Since the ratio is constant, this sequence can be considered a geometric sequence with a common ratio of $1$ .
Arithmetic and Geometric Sequence Conclusion: Since the sequence satisfies the conditions for both an arithmetic sequence (constant difference) and a geometric sequence (constant ratio), the sequence is both an arithmetic and geometric sequence.