Question

Which of the following represents an arithmetic sequence?

The temperature rises and falls at different rates during the day.
The temperature rises by one degree the first hour and then falls two degrees the second hour.
The temperature rises two degrees the first hour, another two degrees the second hour, and so on.
The temperature rises one degree the first hour, 2 degrees the second hour, 4 degrees the third, and so on.

Answer 1

An arithmetic sequence has the same change (common difference) between consecutive terms.

- 1: "Rises and falls at different rates" — not arithmetic (changes vary).
- 2: +1 then −2 — changes are not equal, so not arithmetic.
- 3: +2 each hour — constant change of 2, so this is arithmetic (common difference 2).
- 4: 1, 2, 4, ... — changes are 1, 2, 4,... not constant, so not arithmetic.

Only the third scenario is an arithmetic sequence.