Question

Solve the question: $-4$+$(-1)$+$2+5+..+x$ = $437$.

Answer 1

$x$ is the $n^{th}$ term of AP, where $a=-4$, $d=-1-(-4)=3$ , $S_n$ $=437$

$S_n=\frac{n}{2}(2a+(n-1\left)d\right)$
$437=$$\frac{n}{2}$$(-8+(n-1\left)3\right)$

$874=-8n+3$$n^2$ $-3n$

3$n^2$ $-11n-874=0$

$\Rightarrow 3n^2-(57-46)n-874=0$

$\Rightarrow 3n^2-57n-46n-874=0$

$\Rightarrow 3n(n-19)-46(n-19)=0$

$\Rightarrow (n-19)(3n-46)=0$

$\Rightarrow n-19=0,3n-46=0$

$\Rightarrow n=19,n=\frac{46}{3}$

​ $\therefore n=19$

So, $x=a+(n-1)d$

$x=-4+3(19-1)$

$x=-4+54$

$x=50$

Hence, this is answer.