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# A sequence is defined by an = (an-2)^2 - (an-1) for all terms n = 2, a

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Magoosh GMAT Instructor
Joined: 28 Dec 2011
Posts: 4487
A sequence is defined by an = (an-2)^2 - (an-1) for all terms n = 2, a  [#permalink]

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03 Mar 2017, 17:28
2
6
00:00

Difficulty:

35% (medium)

Question Stats:

75% (02:24) correct 25% (02:26) wrong based on 118 sessions

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A sequence is defined by $$a_{n} = (a_{n-2})^2 - (a_{n-1})$$ for all terms n > 2, and $$a_1 = 2$$ and $$a_2 = 1$$. What is the value of $$a_7$$?
(A) – 64
(B) – 7
(C) 38
(D) 88
(E) 128

This is the final problem from a set of challenging GMAT Quant practice question. For the whole collection, as well as the OE for this question, see:
Challenging GMAT Math Practice Questions

Mike

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Mike McGarry
Magoosh Test Prep

Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)
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Joined: 08 Sep 2016
Posts: 110
A sequence is defined by an = (an-2)^2 - (an-1) for all terms n = 2, a  [#permalink]

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03 Mar 2017, 17:58
2
I think the Answer is E.

Did it the brute force way - about 3 minutes
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Joined: 03 Jan 2017
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Re: A sequence is defined by an = (an-2)^2 - (an-1) for all terms n = 2, a  [#permalink]

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03 Mar 2017, 20:28
1
Put the values in equation.
a1 =2
a2=1
a3=3
a4=-2
a5=11
a6=-7
a7=128. Ans. E

Hit kudos if you like...

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Re: A sequence is defined by an = (an-2)^2 - (an-1) for all terms n = 2, a  [#permalink]

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16 Mar 2017, 22:50
a1 =2;a2=1;a3=3;a4=-2;a5=11;a6=-7;a7=128, keep values to get the series , Hit Kudos if you liked it.
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Re: A sequence is defined by an = (an-2)^2 - (an-1) for all terms n = 2, a  [#permalink]

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17 Mar 2017, 01:17
a1 =2
a2=1
a3=3
a4=-2
a5=11
a6=-7
a7=128.

Option E
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Re: A sequence is defined by an = (an-2)^2 - (an-1) for all terms n = 2, a  [#permalink]

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07 Feb 2018, 02:54
a3= 4-1 = 3
a4= 1-3= -2
a5= 9 + 2= 11
a6= 4-11 = -7
a7= 121 + 7 = 128
Option E

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Re: A sequence is defined by an = (an-2)^2 - (an-1) for all terms n = 2, a  [#permalink]

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19 Mar 2018, 20:12
mikemcgarry wrote:
A sequence is defined by $$a_{n} = (a_{n-2})^2 - (a_{n-1})$$ for all terms n > 2, and $$a_1 = 2$$ and $$a_2 = 1$$. What is the value of $$a_7$$?
(A) – 64
(B) – 7
(C) 38
(D) 88
(E) 128

This is the final problem from a set of challenging GMAT Quant practice question. For the whole collection, as well as the OE for this question, see:
Challenging GMAT Math Practice Questions

Mike

a3 = (a1)^2 - (a2)
= 3

a4 = (a2)^2 - (a3)
= -2

a5 = (a3)^2 - (a4)
= 11

a6 = (a4)^2 - (a5)
= -7

a7 = (a5)^2 - (a6)

thanks
Re: A sequence is defined by an = (an-2)^2 - (an-1) for all terms n = 2, a   [#permalink] 19 Mar 2018, 20:12
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