Let the sum of the first three terms of an AP be 39 and the sum of its last four terms be 178

Let the sum of the first three terms of an A.P. be 39 and the sum of its last four terms be 178. If the first term of this A.P. is 10, then the median of the A.P. is:

  1. 26.5
  2. 28
  3. 29.5
  4. 31

Solution

The first term of this A.P. is 10. Sum of the first three terms is

10 + (10+d) + (10+2d) = 39

30 + 3d = 39

d = 3

Tn = 10 + (n–1)3 = 3n + 7

Sum of last four terms = 178

(3n+7) + (3n–3+7) + (3n–6 +7) + (3n–9 +7) = 178

12n + 10 = 178

n = 14

Median = (7th term + 8th term)/2

= (28+31)/2 = 29.5

The correct option is C.