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Function Question - Princenton Review

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Function Question - Princenton Review

by marreroj » Wed Sep 16, 2009 1:02 pm
Can anyone help with the following function question from a Princeton Review CAT test?

The nth term of a sequence a1, a2, a3... is given by the equation an =(an-1)^2 +n. If a3-(a1)^4 = 31, what is a2?

(a) 6
(b) 8
(c) 14
(d) 15
(e) 16

Thanks!
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by truplayer256 » Wed Sep 16, 2009 5:05 pm
an=(an-1)^(2)+n

a3-(a1)^(4)=31--->(1)

a3=(a2)^(2)+3--->(2)

a2=(a1)^(2)+2--->(3)

Substitute into 2.

a3=[(a1)^(2)+2]^(2)+3

a3=(a1)^(4)+4(a1)^(2)+7

Substitute into 1.

(a1)^(4)+4(a1)^(2)+7-(a1)^(4)=31

4(a1)^(2)+7=31

(a1)^(2)=6

Substitute into 3 to find a2.

a2=6+2=8

B should be your answer.
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by marreroj » Wed Sep 16, 2009 5:35 pm
Thanks!
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