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JEE Main 202622 JanuaryMorning Shift
Exam
JEE Main
Year
2026
Date
22 January
Shift
Morning Shift
Subject
Mathematics
Chapter
Sequences and Series

JEE Main 2026 · 22 January · Morning Shift · Mathematics · Sequences and Series

If the sum of the first four terms of an A.P. is 6 and the sum of...

If the sum of the first four terms of an A.P. is 6 and the sum of its first six terms is 4, then the sum of its first twelve terms is

Options

  1. A-22
  2. B-24
  3. C-20
  4. D-26

Correct answer

A. -22

Step-by-step solution

S4=6⇒2(2a+3d)=6⇒2a+3d=3S_4 = 6 \Rightarrow 2(2a+3d) = 6 \Rightarrow 2a+3d = 3 ...(i)
S6=4⇒3(2a+5d)=4⇒2a+5d=43S_6 = 4 \Rightarrow 3(2a+5d) = 4 \Rightarrow 2a+5d = \frac{4}{3} ...(ii)
(ii) −- (i): 2d=43−3=−53⇒d=−562d = \frac{4}{3} - 3 = -\frac{5}{3} \Rightarrow d = -\frac{5}{6}.
From (i): 2a=3+52=1122a = 3 + \frac{5}{2} = \frac{11}{2}.
S12=6(2a+11d)=6(112−556)=6×−226=−22S_{12} = 6(2a + 11d) = 6\left(\frac{11}{2} - \frac{55}{6}\right) = 6 \times \frac{-22}{6} = -22.
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