Home » An arithmetic progression has first term 11 and fourth term 32. The sum of the…

An arithmetic progression has first term 11 and fourth term 32. The sum of the…

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
sn = n(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