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Algebra
Arithmetic Progressions
jee_main_2026_april_8_shift_1
Grade None

Question:

The sum of the first 4 terms of an AP is 32 and the sum of the first 8 terms is 96. Find the common difference.
A. 1
B. 2
C. 3
D. 4

Step-by-Step Solution

Key Concept: Use S₄ = 4/2[2a + 3d] = 32 and S₈ = 8/2[2a + 7d] = 96.
Step 1: S₄ = 4/2[2a + 3d] = 32 => 2a + 3d = 16 ...(1). Step 2: S₈ = 8/2[2a + 7d] = 96 => 2a + 7d = 24 ...(2). Step 3: Subtract (1) from (2): 4d = 8 => d = 2.
Correct Answer: B
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