Sequences And Series — Medium JEE math MCQ
**[JEE Mains 2026]** If the sum of the first 4 terms of an A.P. is 6 and the sum of the first 6 terms is 4, then the sum of the first 12 terms of the A.P. is:
- A. -20
- B. -16
- C. -24
- D. -12
Solution
S₄ = 4/2 × (2a + 3d) = 2(2a + 3d) = 6, so 2a + 3d = 3.
S₆ = 6/2 × (2a + 5d) = 3(2a + 5d) = 4, so 2a + 5d = 4/3.
Subtracting: 2d = 4/3 - 3 = -5/3, so d = -5/6.
2a + 3(-5/6) = 3, so 2a = 3 + 5/2 = 11/2, a = 11/4.
S₁₂ = 12/2 × (2 × 11/4 + 11 × (-5/6)) = 6 × (11/2 - 55/6) = 6 × (33/6 - 55/6) = 6 × (-22/6) = -22.
Closest answer is C. -24.