Question

The sum of the first $16$ terms of an AP whose first term and the third term are $5$ and $15$ respectively is

Answer 1

Correct Answer: 680

Explanation:
$1^{\text{st }}$ Method$1^{\text{st }}\text{ term }=5$$3^{\text{rd }}\text{ term }=15$$\text{ Then, }d=5$${16}^{\text{th }}\text{ term }=a+15d$$=5+15\times 5=80$$\text{ Sum }=n\times \frac{(a+l)}{2}$$=\text{ no. of terms }\times \frac{\text{ first term }+\text{ last term }}{2}$$=16\times \frac{(5+80)}{2}$$=16\times \frac{85}{2}$$=8\times 85$$=680$$2^{\text{nd }}$ Method(Thought Process). Sum $=$ number of terms $x$ average of that $\mathrm{AP}$$\mathrm{Sum}=16\times \frac{(5+80)}{2}$$=16\times \frac{85}{2}$$=8\times 85$$=680$Hence, the correct answer is 680.