Full solution

Q. What kind of sequence is this?

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429, 429, 429, 429, \dots

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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 Definition: An arithmetic sequence is a sequence of numbers with the difference between any two consecutive terms being constant. This difference is called the common difference. $\newline$ To check if the given sequence is arithmetic, we calculate the difference between consecutive terms. $\newline$ Difference = $429 - 429 = 0$
Check for Arithmetic Sequence: Since the difference between consecutive terms is constant ( $0$ in this case), the sequence is an arithmetic sequence.
Geometric Sequence Definition: 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. $\newline$ To check if the given sequence is geometric, we calculate the ratio between consecutive terms. $\newline$ Ratio = $\frac{429}{429} = 1$
Check for Geometric Sequence: Since the ratio between consecutive terms is constant ( $1$ in this case), the sequence is also a geometric sequence.
Conclusion: The given sequence is both an arithmetic sequence (with a common difference of $0$ ) and a geometric sequence (with a common ratio of $1$ ).