Question

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

Answer 1

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

Answer 2

arithmetic is an=a1+d(n-1)
a1=first term
an=nth term
d=common difference
n=which term

so
first term is -13
the next term is -8 which is 5 more than -13 so each term is 5 more than the previous, the common difference is 5
so
an=-13+5(n-1)
that is one equation
another one is
an=5n-18 (same equation but expanded and simplified)