Arithmetic progression. I have to find out the first term and the ratio! We know the third term = 8 and the seventh term of progression= 20.

Formula of arithmetic progression of the nth term would be:

an=a1+(n-1)s

where a1: the initial term of an arithmetic progression

s: common difference of successive numbers

You know the third term is 8 so:

8= a1+(3-1)s

8=a1+2s

You know that the seventh term is 20 so:

20= a1+(7-1)s - eqn 1

20=a1+6s - eqn 2

Subtract eqn 1 from eqn 2

20-8=a1-a1+6s-2s

12=4s

4s=12

s=3//

So, use this value and substitute into eqn 2

20= a1+6(3)

a1+18=20

a1=20-18

a1=2//

The first term would be 2