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Algebra
Arithmetic Progressions
jee_main_2026_april_6_shift_2
Grade None

Question:

The sum of the first 3 terms of an AP is 18 and the sum of the first 6 terms is 63. Find the common difference.
A. 2
B. 3
C. 4
D. 5

Step-by-Step Solution

Key Concept: Use S₃ = 3/2[2a + 2d] = 18 and S₆ = 6/2[2a + 5d] = 63.
Step 1: S₃ = 3/2[2a + 2d] = 18 => 2a + 2d = 12 => a + d = 6 ...(1). Step 2: S₆ = 6/2[2a + 5d] = 63 => 2a + 5d = 21 ...(2). Step 3: From (1): a = 6 - d. Substitute in (2): 2(6 - d) + 5d = 21 => 12 - 2d + 5d = 21 => 3d = 9 => d = 3.
Correct Answer: B
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