Question

The first tern of an A.P. is 2 and the 6th term is 12. Find the

sum of the first 12 terms.

Answer 1

For the 2nd and 6th terms, we have:

$$a_2=a_1+d(2-1)=a_1+d,\\ a_6=a_1+d(6-1)=a_1+5d;\\ d=2.5,\\ a_1=-0.5.$$

The sum:

$$\Sigma=\frac n2(2a_1+d(n-1))=\\\space\\ =\frac{12}{2}(2·(-0.5)+2.5(12-1))=159.$$