Question

The sum of the first n terms of an AP whose first term is 8 and the common difference is 20 is equal to the sum of the first 2n terms of another AP, whose first term is - 30 and the common difference is 8. find n?

Answer 1

Given: $a_1=8,d_1=20,a_2=-30,d_2=8$

Sum of first ${}^{\prime }{n}^{\prime }$ terms is given by $S_n=\frac{n}{2}[2a+(n-1)\times d]$

$S_1=S_2$ [given]

$\Rightarrow \frac{n}{2}[2\times 8+(n-1)\times 20]=\frac{2n}{2}[2\times (-30)+(2n-1)\times 8]$

$\Rightarrow 16+20n-20=2(-60+16n-8)$
$\Rightarrow -4+20n=2(-68+16n)$
$\Rightarrow -2+10n=-68+16n$
$\Rightarrow 66=6n$
$\Rightarrow n=11$