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…

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. 29.5
  3. 28
  4. 31

Solution

Let the A.P. be a, a+d,a+2d⋯⋯,l-3d, l-2d, l-d,l
Where a is the first term and l is the last term,
Sum of 1st, 3terms is, 39.
30+3d=39 as a=10 (Given)
d=93=3
Sum of last 4 terms is178.
4l-6d=178
l=49
10, 13, 16, 19.......46, 49
Let number of terms are, n then nthterm is10 + (n - 1) 3 = 49
⇒n = 14
So the median of the series would be mean of 7th  and 8th term
10+6⋅3+10+7⋅32
=592 =29.5

Alternate way
The median would be mean of 10 and 49, That is 29.5.

Asked in: JEE Main 2015 (10 Apr Online)

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