JEE Main202622 January 2026Morning ShiftMathematicsSequences and SeriesActual

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

A-22
B-24
C-20
D-26

Correct answer

A. -22

Step-by-step solution

S₄ = 6 2(2a+3d) = 6 2a+3d = 3 ...(i) S₆ = 4 3(2a+5d) = 4 2a+5d = 4 3 ...(ii) (ii) - (i): 2d = 4 3 - 3 = - 5 3 d = - 5 6 . From (i): 2a = 3 + 5 2 = 11 2 . S₁₂ = 6(2a + 11d) = 6 ( 11 2 - 55 6 ) = 6 -22 6 = -22 .

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