JEE Main 2015MathematicsSequences and SeriesEasyMCQ

JEE Main 2015 — Sequences and Series Question with Solution

JEE Main 2015 (10 Apr Online)

Question

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 :

Choose an option

Show full solutionCorrect option: B
Correct answer
B29.5

Step-by-step explanation

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.

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About this question

This is a previous-year question from JEE Main 2015, covering the Sequences and Series chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.