Question

Find $S_{21}$ of an A.P. whose middle term is $20$.

Answer 1

Given,

middle term $t_{11}=20$

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

$t_{11}=a+10d=20$

$\Rightarrow a=20-10d$

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

$S_{21}=\frac{21}{2}\left[2\right(20-10d)+(21-1\left)d\right]$

$=\frac{21}{2}\left[40\right]$

$\therefore S_{21}=420$