Question

If a number is multiplied by each term of an arithmetic sequence, is the resulting sequence still arithmetic of is it geometric?

Answer 1

By definition, an arithmetic sequence is a sequence of numbers where each term after the first is found by adding to the previous one a fixed, non-zero number called the difference.

Example: `a, a+d, a+2d, ...`

Let `m` be a constant number that is multiplied by each element of the arithmetic sequence. The resulting sequence will be:
`ma, ma + md, ma + 2md`

We notice that the new sequence is an arithmetic one, with a new difference `md` instead of `d`.