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Mathematics > Standard Multiple Choice

Read the following SAT test question and then click on a button to select your answer. 

3, 6, 11,18, ...

The first four terms of a sequence are shown above. Which of the following could be the formula that gives the nth term of this sequence for all positive integers n?

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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 comma 3 comma and 4. If n = 1, then 2 times 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 (2 times n) + 1 = 7 and 3 times n = 9, but the third term of the sequence is 11, so the general formula cannot be (2 times n) + 1 or 3n. However, for n = 1 comma 2 comma 3 comma 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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