Question

If $1^{st}$ and $2^{nd}$ terms of an A.P. are $1$ and $-3$ respectively, find the nth term and the sum of the first n terms.

Answer 1

$1^{st}term=a,2^{nd}term=a+d$ where $a=1,a+d=-3$,
$\Rightarrow d=-4$ (common difference of A.P.)
$\Rightarrow a_n=a+(n-1)d=1+(n-1)(-4)=5-4n$.
and $S_n=\frac{n}{2}\{a+a_n\}=\frac{n}{2}\{1+5-4n\}=n(3-2n)$.