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Algebra
Arithmetic Progressions
jee_main_2026_april_6_shift_1
Grade None

Question:

The sum of the first 5 terms of an AP is 35 and the sum of the first 10 terms is 120. Find the common difference.
A. 1
B. 2
C. 3
D. 4

Step-by-Step Solution

Key Concept: Use S₅ = 5/2[2a + 4d] = 35 and S₁₀ = 10/2[2a + 9d] = 120.
Step 1: S₅ = 5/2[2a + 4d] = 35 => 2a + 4d = 14 => a + 2d = 7 ...(1). Step 2: S₁₀ = 10/2[2a + 9d] = 120 => 2a + 9d = 24 ...(2). Step 3: From (1): a = 7 - 2d. Substitute in (2): 2(7 - 2d) + 9d = 24 => 14 - 4d + 9d = 24 => 5d = 10 => d = 2.
Correct Answer: B
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