Question

Given an arithmetic sequence in the table below, create the explicit formula and list any restrictions to the domain.

n an
1 40
2 47
3 54

Answer 1

an=a1+d(n-1)
an=nth term
a1=first term, when n=1
d=common differnce=amount each term increases by
n=which one


so
when n=1, an=40
so a1=40
it seems to increas by 7 each time

an=40+7(n-1)
explicit formula is expanded
an=40+7n-7
an=33+7n is the formula

the domain is natural numbers because you can't have the -3rd term or the 0th term or the 3.24th term

domain is natural numbers
the formula is
`a_n=33+7n` or
`a_n=7n+33`