Class 11

Math

Co-ordinate Geometry

Straight Lines

Find the $n_{th}$ term and sum to $n$ terms of the following series:

$2+6+12+20+$____

As we can see that the general term is $r(r+1)$

so, the $n_{th}$ term is $n(n+1)$

Sum of given series upto $n$ terms:

$⇒r=1∑n r(r+1)$

$=r=1∑n r_{2}+r=1∑n r$

$=6n(n+1)(2n+1) +2n(n+1) $

$=2n(n+1) {32n+1 +1}$

$=2n(n+1) 32n+4 $

$=3n(n+1)(n+2) $