Question

The nth term of an A.P. is p and the sum of the first n terms is s. The first term is

• A. $\frac{2p+sn}{n}$
• B. $\frac{2p-sn}{n}$
• C. $\frac{2s+pn}{n}$
• D. $\frac{2s-pn}{n}$

Answer 1

The correct option is D $\frac{2s-pn}{n}$

Let first term of A.P. be a

$\text{Then},\frac{n}{2}(a+p)=s$

$=an+pn=2s$

$=an=2s-pn$

$\Rightarrow a=\frac{2s-pn}{n}$

$\therefore$ option $D$ is correct