NTA Abhyas JEE Main2020MathematicsSequences and SeriesPractice

If 5 + 9 + 13 + … n terms 7 + 9 + 11 + … n + 1 terms = 17 16 , then n is equal to

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Correct answer

A. 7

Step-by-step solution

5 + 9 + 13 + … n terms 7 + 9 + 11 + … n + 1 terms ⇒ n 2 2 × 5 + n - 1 4 n + 1 2 2 × 7 + n + 1 - 1 2 = 17 16 ⇒ n 4 n + 6 n + 1 2 n + 14 = 17 16 ⇒ n ( 2 n + 3 ) n + 1 n + 7 = 17 16 ⇒ 2 n 2 + 3 n n 2 + 8 n + 7 = 17 16 ⇒ 32 n 2 + 48 n = 17 n 2 + 136 n + 119 ⇒ 15 n 2 - 88 n - 119 = 0 ⇒ n - 7 15 n + 17 = 0 ⇒ n = 7

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