Question

How many terms of the series $18+15+12+.......$ when added together will give $45$?

Answer 1

Given series $18,15,12,....$ is a decreasing A.P. with first term $=a=18$ and $d=-3$

Let number of terms added together to give sum $45$ be $n$

$\Rightarrow 45=\frac{n}{2}\left[2\right(18)+(n-1\left)\right(-3\left)\right]$

$\Rightarrow 90=n(39-3n)$

$\Rightarrow 3n^2-39n+90=0$

On solving this quadratic equation, we get $n=10,3$