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

A. 600 B. 765 C. 640 D. 680 Answer: Option D
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Solution(By Apex Team)

$\begin{array}{l}1^{\text{st }}\text{ Method : }\\ 1^{\text{st }}\text{ term }=5\\ 3^{\text{rd }}\text{ term }=15\\ \text{ Then, }d=5\\ 16^{\text{th }}\text{ ; term }=a+15d\\ =5+15\times5=80\end{array}$ $\begin{aligned}&\text{ Sum }=n\times\frac{(a+l)}{2}\\ &=\text{ no. ofterms }\times\frac{\text{ first term }+\text{ last term }}{2}\\ &=16\times\frac{(5+80)}{2}\\ &=16\times\frac{85}{2}\\ &=8\times85\\ &=680\end{aligned}$ 2nd Method(Thought Process): Sum = number of terms × average of that AP $\begin{aligned}\text{ Sum }&=16\times\frac{(5+80)}{2}\\ &=16\times\frac{85}{2}\\ &=8\times85\\ &=680\end{aligned}$

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