Find an equation for the nth term of the arithmetic sequence. -13, -8, -3, 2

Any arithmetic sequence can be expressed as:

a(n)=a+d(n-1), a(n)=nth term, a=initial term, d=common difference, n=term no.

Find the common difference.

-8--13=-3--8=2--3=d=5

The first term is -13 so a=-13, so our rule is:

a(n)=-13+5(n-1)

The above is what they might have, but it can be simplified further...

a(n)=-13+5n-5

a(n)=5n-18