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

1 Answer
Alex Boroda
Jun 1, 2015

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#.

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