Question

If a fixed number is added to each term of an arithmetic​ sequence, is the resulting sequence an arithmetic​ sequence? explain

Answer 1

Yes.

Explanation:

If we add a fixed number to each term of an arithmetic sequence, we are still going to be having an arithmetic sequence.

For example, given the following sequence:

1, 3, 5, 7, 9, 11...

The difference between consecutive terms is 2, therefore the pattern is adding two to the previous term.

If we add a fix number, let's say '3':

1+3, 3+3, 5+3, 7+3, 9+3, 11+3...

4, 6, 8, 10, 12, 14...

We notice that the pattern is the same, and it's still an arithmetic sequence.