Question

If the sum of the first $14$ terms of an AP is $1050$ and its first term is $10$, find the ${20}^{th}$ term.

Answer 1

$S_{14}=1050$

$a=10$

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

$1050=\frac{14}{2}[2\times 10+(14-1\left)d\right]$

$\frac{1050}{7}=[20+14d-d]$

$150-20=13d$

$130=13d$

$d=10$

The ${20}^{th}$ term is

$a_{20}=a+(n-1)d$

$=10+(20-1)10$

$\Rightarrow 10+190$

$a_{20}\Rightarrow 200$