An arithmetic progression has first term 11 and fourth term 32. The sum of the first nine terms is

A.
351 
B.
531 
C.
135 
D.
153
Correct Answer: Option A
Explanation
1st term a = 11, 4th term = 32
nth term = a + (n – 1)d
4th term = 11 = (4 – 1)d
= 11 + 3d
= 32
3d = 21
d = 7
s_{n} = n(2a + (n – 1)d)
s_{n} = (frac{9}{2})(2 times 11) + (9 – 1)7
(frac{9}{2})(22 + 56) = (frac{9}{2}) x 78
= 351