If the sum of the first n terms of the series 3 + 75 + 243 + 507 + … is 435 3 , then n equals:

Question

If the sum of the first n terms of the series 3 + 75 + 243 + 507 + … is 435 3 , then n equals:, 13, 15, 29, 18

MARKS App · Accepted Answer

3 1 + 25 + 81 + 169 + … = 435 3 3 1 + 5 + 9 + 13 + … T n = 435 3 = 3 × n 2 2 + n - 1 4 = 435 3 = 2 n + 4 n 2 - 4 n = 870 = 4 n 2 - 2 n - 870 = 0 = 2 n 2 - n - 435 = 0 n = 1 ± 1 + 4 × 2 × 435 4 = 1 ± 59 4 ∵ n is + v e ∴ n = 1 + 59 4 =15

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