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Algebra
Arithmetic Progressions
jee_main_2026_april_8_shift_2
Grade None

Question:

The sum of the first 6 terms of an AP is 72 and the sum of the first 12 terms is 216. Find the common difference.
A. 1
B. 2
C. 3
D. 4

Step-by-Step Solution

Key Concept: Use S₆ = 6/2[2a + 5d] = 72 and S₁₂ = 12/2[2a + 11d] = 216.
Step 1: S₆ = 6/2[2a + 5d] = 72 => 2a + 5d = 24 ...(1). Step 2: S₁₂ = 12/2[2a + 11d] = 216 => 2a + 11d = 36 ...(2). Step 3: Subtract (1) from (2): 6d = 12 => d = 2.
Correct Answer: B
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