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Harold did $8$ sit-ups on Tuesday, $4$ sit-ups on Wednesday, $2$ sit-ups on Thursday, and $1$ sit-up on Friday. What kind of sequence is this? $\newline$ Choices: $\newline$ (A) arithmetic $\newline$ (B) geometric $\newline$ (C) both $\newline$ (D) neither

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Identify arithmetic and geometric sequences

Full solution

Q. Harold did

8

sit-ups on Tuesday,

4

sit-ups on Wednesday,

2

sit-ups on Thursday, and

1

sit-up on Friday. What kind of sequence is this?

\newline

Choices:

\newline

(A) arithmetic

\newline

(B) geometric

\newline

(C) both

\newline

(D) neither

List Order: Harold did $8$ sit-ups on Tuesday, $4$ sit-ups on Wednesday, $2$ sit-ups on Thursday, and $1$ sit-up on Friday. Let's list the number of sit-ups in the order they were done. $\newline$ Sequence: $8, 4, 2, 1$
Consecutive Differences: Are the differences between consecutive terms equal? $\newline$ $4 - 8 = -4$ $\newline$ $2 - 4 = -2$ $\newline$ $1 - 2 = -1$ $\newline$ The differences are not the same; therefore, it is not an arithmetic sequence.
Consecutive Ratios: Are the ratios of consecutive terms equal? $\newline$ $\frac{4}{8} = 0.5$ $\newline$ $\frac{2}{4} = 0.5$ $\newline$ $\frac{1}{2} = 0.5$ $\newline$ The ratios are the same; therefore, it is a geometric sequence.
Sequence Type: Since the sequence has a common ratio but not a common difference, it is a geometric sequence.

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