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

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