Question

If the sum of the series $24,20,16,....$ is $60$.Find the number of terms in the series.

Answer 1

Formula,

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

Given,

$S_n=60,a=24,d=20-24=-4$

$60=\frac{n}{2}\left[2\right(24)+(n-1\left)\right(-4\left)\right]$

$120=n[48-4n+4]$

$4n^2-52n+120=0$

$\Rightarrow n^2-13n+30=0$

$(n-10)(n-3)=0$

$\therefore n=3,10$