Question

1,5,9,13,17 is this an arithmetic sequence

Answer 1

We know that all adjacent terms in an arithmetic sequence differ by the same amount, and that amount is called the common difference. Here, we can observe the pairwise difference between the adjacent terms in the sequence:

`image`

So, we see that the difference is always 4 so it is an arithmetic sequence. In fact, the sequence is:

`a_(n)=4n-3`

Answer 2

An arithmetic sequence is a pattern where the number at index n is equal to the number at index n-1 plus value v

Looking at the sequence, we see that there is a pattern of +4 each time

this means we can write it as a formula, where v is 4

[n] = [n-1] + 4

This means it IS an arithmetic sequence