The correct answer is E
Explanation
If a formula gives the nth term of the sequence for all positive integers n, it must give the nth term of the sequence for n = 1 comma 2 ,3 ,and 4. If n = 1, then 2 n = 2 and (n^2) + 1 = 2, but the first term of the sequence is 3, so the general formula cannot be 2 times n or (n^2) + 1. Also, if n = 3, then (2n) + 1 = 7 and 3 times n = 9, but the third term of the sequence is 11, so the general formula cannot be (2n) + 1 or 3n. However, for n = 1 ,2 ,3 , and 4, the values of (n^2) + 2 are 3, 6, 11, 18, respectively. Therefore, the general formula for this sequence could be (n^2) + 2.
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