每日一题

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?

(A) 2n
(B) (2n) + 1
(C) 3n
(D) (n^2) + 1
(E) (n^2) + 2

答案和解析

答案：E

解析：

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 = 1,2,3,and 4. If n = 1, then 2n = 2 and (n^2) + 1 = 2, but the first term of the sequence is 3, so the general formula cannot be 2n or (n^2) + 1. Also, if n = 3, then (2n) + 1 = 7 and 3n = 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.