Question

If the first, second and the last terms of an AP are a, b, c respectively, then the sum is

• A.
• B.
• C.
• D.

Answer 1

The correct option is C

We have, first term = a $\therefore T_1=a$
Second term = b $\therefore T_2=b$
Then, common difference $d=T_2-T_1=b-a$
Also, last term = c
$c=a+(n-1)d\Rightarrow n=\frac{c-a+d}{d}$
$\Rightarrow n=\frac{(b+c-2a)}{(b-a)}[\because d=b-a]\therefore Sumofnterms{S}_n=\frac{n}{2}(2a+(n-1\left)d\right)=\frac{(b+c-2a)(a+c)}{2(b-a)}$