JEE Main 2024 Mathematics question

MathematicsSequence and SeriesJEE Main 2024

Let Sₙ be the sum to n-terms of an arithmetic progression 3, 7, 11, ...... . If , then n equals .

Answer: 9

Solution

Sₖ = (k/2)[6 + (k − 1)4] = k(2k + 1) = 2k² + k. Then Σ Sₖ = 2n(n + 1)(2n + 1)/6 + n(n + 1)/2, so

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Question ID VK-017007