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.

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Answer 1

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

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

Substituting the values we have,

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

$\Rightarrow 1050=140+91d$

$\Rightarrow 910=91d$

$\Rightarrow d=10$

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

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