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Find the sum of the first n terms of the series 2, 5, 14, 41,...

1. 3^(n-1)+8n-3
2. 8·3ⁿ + 4n - 8
3. 3^(n+1) + 8/3 n + 1
4. None of these

Correct answer: None of these

Solution

Differences are 3,9,27,... so a_k = 2 + (3^k-3)/2 = (3^k+1)/2. Summing n terms: S_n = (3^(n+1)-3)/4 + n/2, which equals none of the listed expressions, so the answer is None of these.

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