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

blackdivcp 2022-10-22 Answered
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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Answers (1)

cesantedz
Answered 2022-10-23 Author has 12 answers
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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