Full solution

Q. What kind of sequence is this?

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884, 884, 884, 884, \dots

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Choices:

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(A) arithmetic

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(B) geometric

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(D) neither

Check Constant Difference: 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. Let's check if the given sequence has a constant difference. $\newline$ Difference between terms: $884 - 884 = 0$
Identify Arithmetic Sequence: Since the difference between any two consecutive terms is $0$ , which is constant, the sequence can be considered an arithmetic sequence with a common difference of $0$ .
Check Common Ratio: 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 common ratio. Let's check if the given sequence has a common ratio. $\newline$ Ratio between terms: $\frac{884}{884} = 1$
Identify Geometric Sequence: Since the ratio between any two consecutive terms is $1$ , which is constant and non-zero, the sequence can be considered a geometric sequence with a common ratio of $1$ .
Final Conclusion: The sequence is both an arithmetic sequence with a common difference of $0$ and a geometric sequence with a common ratio of $1$ . Therefore, the correct choice is $(C)$ both.