Question

Solve the equation for $x$: $1+4+7+10+.........+x=287$

Answer 1

Given,

let there be n terms in the A.P

$\frac{n}{2}\left[2\right(1)+(n-1\left)\right(3\left)\right]=287$

$\Rightarrow n(2+3n-3)=574$

$\Rightarrow 2n+3n^2-3n-574=0$

$\Rightarrow 3n^2-n-574=0$

$\Rightarrow 3n^2-42n+41n-574=0$

$\Rightarrow 3n(n-14)+41(n-14)=0$

$\Rightarrow (3n+41)(n-14)=0$

$\Rightarrow n-14=0$

$n=14$

and,

$3n+41=0$

$3n=-41$

$n=\frac{-41}{3}$

$\therefore n=14$

$x=a_{14}=a+(14-1)3$

$=1+13\left(3\right)$

$=40$