Question

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

Answer 1

$Sn=n/2[2a+(n-1\left)d\right]$

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

$287\times 2=n[2+3n-3]$

$574=n[3n-1]$

$574=3n^2-n$

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

Using this formula $\to$

$\beta =(-b\pm \sqrt{b^2-4ac})/2a$

$n=84/6$

$n=14$

So, n is 14th term

$a_n=a(n-1)d$

$=1+(14-1)3$

$=1+13\times 3$

$=40$

$[x=40]$