Question

Find the general term of the arithmetic sequence if a8=8, a20=44

Answer 1

`a_n=3n-16`

Explanation:

`a_n=a_1+(n-1)d\\\\a_8=a_1+(8-1)d\rightarrow 8=a_1+7d\\a_(20)=a_1+(20-1)d\rightarrow 44=a_1+19d`

`-36=-12d\\3=d`

`8=a_1+7(3)\\8=a_1+21\\-13=a_1`

`a_n=-13+(n-1)(3)\\a_n=-13+3n-3\\a_n=3n-16`