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

##### 1 Answer
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: $a , a + d , a + 2 d , \ldots$

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

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