Question

How many terms of the A.P :
$-2,-7,-12,...$ will give the sum $-780$. Also find the last term.

Answer 1

$-2,-7,-\mathrm{12........}$

sum $=-780$

sum $=[2a+(n-1\left)d\right]\frac{n}{2}$

$-780\times 2=[-4+5n+5]n/2$

$-1560=(1-n{)}^n$

$n^2-n-1560=0$

$n^2-40n+{39}^n-1560=0$

$n(n-40)+39(n-40)=0$

$(n-40)(n+39)=0$

$2\frac{40}{2}[-4+leastterm]=-780$

$-4+l=-39$

$l=-35$