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.

• A. 500
• B. 400
• C. 200
• D. 300

Answer 1

The correct option is C 200

Let $S_n$ be the sum of first n terms of an A.P.

Here,
n = 14 and given $S_{14}=1050$ ,
a = 10

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

Plugging in the values, we get,

$1050=\left(\frac{14}{2}\right)[20+13d]$

$\Rightarrow 1050=140+91d$

$\Rightarrow 910=91d$

$\Rightarrow d=10$

$\therefore a_{20}=10+(20–1)\times 10=200$

i.e.
${20}^{th}$ term is 200.