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

Question

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.

ID: 100402

bM22 · Accepted Answer

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

Sajjad1994 · Answer

Official Explanation https://gmatclub.com/forum/download/file.php?mode=view&id=63320 3.jpg

ashwani1984 · Answer

S1 and S4 are related with relation --->

S1(sq2) + S4 = 2

Apt0810 · Answer

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

Posted from my mobile device

mSKR · Answer

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

sayan640 · Answer

KarishmaB   GMATinsight   chetan2u  WOuld you like to explain this question ?

KarishmaB · Answer

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/

bumpbot · Answer

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

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\(s_{1}\)	\(s_{4}\)	Values
		-12
		-7
		-3
		-1
		0

GMAT Two-part Analysis (TPA) Questions

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

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