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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Function Question - Princenton Review
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truplayer256
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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.
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.
