Question

Find the sum of n terms of AP$18,15\frac{1}{2},13,.$.

Answer 1

Given,

$a=18$

$d=\frac{31}{2}-18=-\frac{5}{2}$

Formula,

$a_n=a+(n-1)d$

$=18+(n-1)(-\frac{5}{2})$

$a_n=\frac{41-5n}{2}$

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

$=\frac{n}{2}\left[2\right(18)+(n-1\left)(-\frac{5}{2})\right]$

$=\frac{n}{2}\left[\frac{41-5n}{2}\right]$

$S_n=\frac{41n-5n^2}{4}$