Let the sum of the first three terms of an A.P. be 39

• Sequences Series

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. 31
2. 29.5
3. 28
4. 26.5

Answer

The first term of this A.P. is 10.

Sum of the first three terms = 10 + (10+d) + (10+2d) = 39

d = 3

T_n = 10 + (n–1)3 = 3n + 7

Sum of last four terms = 178

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

n = 14

Median = (7^th term + 8^th term)/2 = (28+31)/2 = 29.5

The correct option is B.