Question

Find the value of $y$ if $1+4+7+10+.....+y=287$

Answer 1

$a=1,d=4-1=3,S_n=287$

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

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

$574=2n+3n^2-3n$

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

solving the above equation, we get,

$\therefore n=14$

$S_n=\frac{n}{2}(a+l)$

$287=\frac{14}{2}(1+y)$

$287=7(1+y)$

$41=1+y$

$\therefore y=40$