Nth term of 1 8 15 22 29

This is an aritmetic sequence where the terms increase by 7

So the common difference d = 7. The first term is 1

nth term = a1 + (n-1) d

= 1 + (n-1) 7

= 7n - 6

This is an arithmetic sequence because each term is 7 greater than the previous term, so 7 is what is called the common difference ...

Any arithmetic sequence can be expressed as:

a (n) = a+d (n-1), a=first term, d=common difference, n=term number.

We know a=1 and d=7 so:

a (n) = 1+7 (n-1)

a (n) = 1+7n-7

a (n) = 7n-6

The above is the "rule" for the nth term.