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JEE Main 202628 JanuaryMorning Shift
Exam
JEE Main
Year
2026
Date
28 January
Shift
Morning Shift
Subject
Mathematics
Chapter
Sequences and Series

JEE Main 2026 · 28 January · Morning Shift · Mathematics · Sequences and Series

The common difference of the A.P.: a_ 1 , a_ 2 , , a_ m is 13 more...

The common difference of the A.P.: a1,a2,…,ama_{1}, a_{2}, \ldots, a_{\mathrm{m}} is 13 more than the common difference of the A.P.: b1,b2,…,bnb_{1}, b_{2}, \ldots, b_{n}. If b31=−277,b43=−385b_{31}=-277, b_{43}=-385 and a78=327a_{78}=327, then a1a_{1} is equal to

Options

  1. A16
  2. B21
  3. C19
  4. D24

Correct answer

C. 19

Step-by-step solution

Let dd and d′d' be the common differences of the two APs respectively.
Given: d=d′+13d = d' + 13.
From the second AP: b43−b31=12d′b_{43} - b_{31} = 12d', so −385−(−277)=12d′-385 - (-277) = 12d', giving −108=12d′-108 = 12d' and d′=−9d' = -9.
Therefore d=−9+13=4d = -9 + 13 = 4.
For the first AP: a78=a1+77da_{78} = a_1 + 77d, so 327=a1+77(4)=a1+308327 = a_1 + 77(4) = a_1 + 308.
Thus a1=19a_1 = 19
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