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

Answer: Option D

$$\begin{array}{rl}& 1^{st}\text{Method}:\\ & 1^{st}\text{term}=5;\\ & 3^{rd}\text{term}=15;\\ & \text{Then},d=5;\\ & 16^{th}\text{term}=a+15d\\ & =5+15\times 5=80\\ & \text{Sum}=n\times \frac{\left(a+l\right)}{2}\end{array}$$
$$=\text{no}\text{.}\text{of}\text{terms}\times \frac{\text{first}\text{term + last}\text{term}}{2}$$
$$\begin{array}{rl}& =16\times \frac{\left(5+80\right)}{2}\\ & =16\times \frac{85}{2}\\ & =8\times 85\\ & =680\end{array}$$

2^nd Method(Thought Process):
Sum = number of terms × average of that AP
$$\begin{array}{rl}& \text{Sum}=16\times \frac{\left(5+80\right)}{2}\\ & =16\times \frac{85}{2}\\ & =8\times 85\\ & =680\end{array}$$