Algebra
Arithmetic Progressions
jee_main_2026_april_4_shift_2
Grade 12
Question:
If the sum of the first n terms of an AP is S_n = 2n^2 + n, and the first term is a, common difference is d, find a + d.
Step-by-Step Solution
Key Concept: First term a = S_1, common difference d = S_2 - 2S_1.
Step 1: a = S_1 = 2(1)^2 + 1 = 3. Step 2: S_2 = 2(4) + 2 = 10. Step 3: d = S_2 - 2S_1 = 10 - 2(3) = 4. Step 4: a + d = 3 + 4 = 7.
Correct Answer: D
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