Question

Find the number of terms of the $AP$ $54,51,48$,. So that their sum is $513$.

Answer 1

Formula:

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

Given,

$513=\frac{n}{2}\left[2\right(54)+(n-1\left)\right(-3\left)\right]$

$1026=n[108-3n+3]$

$3n^2-111n+1026=0$

$(n-19)(n-18)=0$

$\therefore n=19,18$