Question

nth term of 1 8 15 22 29

Answer 1

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

Answer 2

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.