Question

How many terms of the $A.P;24,21,18,...$ must be taken such that their sum is $78$

Answer 1

Formula,

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

Given,

$a=24,d=21-24=-3,S_n=78$

$78=\frac{n}{2}\left[2\right(24)+(n-1\left)\right(-3\left)\right]$

$156=n[48-3n+3]$

$3n^2-51n+156=0$

$n^2-17n+52=0$

$(n-13)(n-4)=0$

$\therefore n=4,13$