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
Verified Correct Answer: A.
Step-by-Step Mathematical Solution
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
sn = \(\frac{n}{2}\)(2a + (n - 1)d)
sn = \(\frac{9}{2}\)(2 \(\times\) 11) + (9 - 1)7
\(\frac{9}{2}\)(22 + 56) = \(\frac{9}{2}\) x 78
= 351
Source: Myschool Past Questions Archive (Record #32708)