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

Answer: Option A

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 :
$$\begin{array}{rl}& \Rightarrow \frac{10}{2}\left[2a+9d\right]=390\\ & \Rightarrow 2a+9d=\mathrm{78.....}(ii)\\ & \Rightarrow a+2d=19\end{array}$$
From equation (i) and (ii)
a = 3
d = 8