The sum of 10 terms of the arithmetic series is 390. If the third term of the series is 19. Find the first term :

A. 3

B. 5

C. 7

D. 8

Answer: Option A

Solution(By Examveda Team)

Sum of A.P. = $$\frac{n}{2}\left[ {2a + (n - 1)d} \right]$$
n^th term = a + (n - 1)d
3^rd term :
⇒ a + (3 - 1)d = 19
⇒ a + 2d = 19.....(i)
Sum of 10 term :
$$\eqalign{ & \Rightarrow \frac{{10}}{2}\left[ {2a + 9d} \right] = 390 \cr & \Rightarrow 2a + 9d = 78..... (ii) \cr & \Rightarrow a + 2d = 19 \cr} $$
From equation (i) and (ii)
a = 3
d = 8