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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**

## Show Answer

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

A. 600B. 765

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D. 680