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发表于 2009-7-25 00:41:12
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本帖最后由 tuziduidui 于 2009-7-26 07:40 编辑
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: r1 F8 w- ?# ]: ]Read the following SAT test question, then click on a button to select your answer.) a. M. q5 r8 Y f D) ` s1 N
3,6,11,18,... |8 I+ Q' l, e
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?0 T. i" ^7 Z' k- O6 D K7 d
A. 2n
0 U6 [- f- C! d# O db. 2n+1: N1 _; q5 Y9 B& i; i6 l
C. 3n
8 ~' s# p+ \2 {+ mD. n^2+1. ^/ ~# C4 W5 S+ v! P6 e
E. n^2+2
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Answer: E
! c; S0 ]+ a3 G- F7 \; D! oHere's Why:
* l) W& h$ v) e6 JIf 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, and 18, receptively. Therefore, the general formula for this sequence could be n^2+2., N& R w4 I& g- g& j+ Q5 g
Difficulty: Medium
8 e: C1 x# d5 e7 C( O6 TQuestion Type: Standard Multiple Choice (Mathematics) |
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