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For each positive integer n, the quantity sn is defined such that sn

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parkhydel
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For each positive integer n, the quantity sn is defined such that sn [#permalink] For each positive integer n, the quantity sn is defined such that sn   14 May 2020, 01:02
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For each positive integer n, the quantity \(s_{n}\) is defined such that \(s_{n + 2} = (s_{n})^2 − s_{n + 1}\). In addition, \(s_{2} = 1\).

Select values for \(s_{1}\) and \(s_{4}\) that are jointly compatible with these conditions. Make only two selections, one in each column.­

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ID: 100402
\(s_{1}\) \(s_{4}\) Values
-12
-7
-3
-1
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\(s_{1}\): -3 \(s_{4}\): -7
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Re: For each positive integer n, the quantity sn is defined such that sn [#permalink] For each positive integer n, the quantity sn is defined such that sn   25 Aug 2021, 08:46
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ashwani1984
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Re: For each positive integer n, the quantity sn is defined such that sn [#permalink] For each positive integer n, the quantity sn is defined such that sn   Updated on: 14 May 2020, 23:00
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S1 and S4 are related with relation --->

S1(sq2) + S4 = 2

Originally posted by ashwani1984 on 14 May 2020, 01:39.
Last edited by ashwani1984 on 14 May 2020, 23:00, edited 1 time in total.
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Re: For each positive integer n, the quantity sn is defined such that sn [#permalink] For each positive integer n, the quantity sn is defined such that sn   14 May 2020, 07:59
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Given: sn+2=(sn)2−sn+1
S2 = 1.

When we substitute values for S3 and S4 we get:
S3 = S1^2 - S2.
S4 = S2^1 - S3 => S4 = S2^1 - S1^2 + S2,
Now Substituting S2 =1, we get:
S4 + S1^2 = 2.

Only 2 values satisfy the given condition: S4 = -7, S1 = -3
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Re: For each positive integer n, the quantity sn is defined such that sn [#permalink] For each positive integer n, the quantity sn is defined such that sn   14 May 2020, 12:39
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Here,

S3= S1^2-S2
S4=S2^2-S3
S4= S2^2-S1^2+S2
Now S2=1
S4=2-S1^2
So checking from options

S4=-7,S1=-3

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Re: For each positive integer n, the quantity sn is defined such that sn [#permalink] For each positive integer n, the quantity sn is defined such that sn   29 May 2020, 18:53
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S4= s2^2-S3
S3=s1^2-1

S4 = s2^2-s1^2+1
S4= 2-s1^2


Values are given in negative it means s4 could be negative it means s1 mode should be higher than 2
Try s1= -3
S2 comes out to be -7
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Re: For each positive integer n, the quantity sn is defined such that sn [#permalink] For each positive integer n, the quantity sn is defined such that sn   16 Jun 2024, 14:50
KarishmaB GMATinsight chetan2u WOuld you like to explain this question ?­
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For each positive integer n, the quantity sn is defined such that sn [#permalink] For each positive integer n, the quantity sn is defined such that sn   16 Jun 2024, 22:20
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parkhydel wrote:
For each positive integer n, the quantity \(s_{n}\) is defined such that \(s_{n + 2} = (s_{n})^2 − s_{n + 1}\). In addition, \(s_{2} = 1\).

Select values for \(s_{1}\) and \(s_{4}\) that are jointly compatible with these conditions. Make only two selections, one in each column.­

Show Spoiler
ID: 100402

­
 \(s_{n + 2} = (s_{n})^2 − s_{n + 1}\)

 \(s_3 = (s_1)^2 − s_2  = (s_1)^2 − 1\)

\(s_4 = (s_2)^2 − s_3 = 1^2 - ((s_1)^2 − 1) = 2 - (s_1)^2 \)

Hence s1 and s4 satisfy this condition:
\(s_4 = 2 - (s_1)^2 \)

If s1 is -3, s4 = -7

ANSWER: -3, -7­

A couple of blog posts on sequences:
https://anaprep.com/algebra-introducing-sequences/
https://anaprep.com/algebra-a-difficult ... sequences/
 
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