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

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/

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 ?

MarkGMATMentor · Answer

On sequence questions, you often need to use the sequence equation twice to get what you need.

But here, what should you set n equal to? Note that only when n = 1 or n = 2 will you get an  s_{2}  term that you can substitute.

Let's set n = 1 and plug in  s_{2}=1 :

s_{3} = (s_{1})^2 – s_{2}

s_{3} = (s_{1})^2 - 1

Then, set n = 2 and re-run the equation:

s_{4} = (s_{2})^2–s_{3}

s_{4} = 1 – s_{3}

Note that  o  n a Two Part Analysis question where you must select two values that are jointly compatible, you want an equation that contains only those two variables.  Then you’ll be able to use the answer choices to solve.

Here you have two simultaneous equations that both contain an  s_{3}  term. So if you put those equations together, you’ll have a new equation with only  s_{1}  and  s_{4} , which is what you want.

Plug the first equation in for  s_{3}  in the second equation:

s_{4} = 1 – ((s_{1})^2 – 1)

s_{4} = 1 – (s_{1})^2 + 1

(s_{1})^2 + s_{4} = 2

Now you can use your answer choices. It’s best to start with one column rather than trying random combinations.

Since  s_{1}  is squared, it’s the easier column to start with.

(-12)^2  is 144, too big for  s_{4}  to be any of the choices.

(-7)^2  is 49, also too big.

(-3)^2  is 9. This works when  s_{4}  is -7. Your answers are  s_{1}= -3  and  s_{4} = -7 .

Remember, you often need to run the sequence equation twice (or more) to get what you need. And on “jointly compatible” TPA questions, what you need is an equation that contains the two variables that match the answer choices.

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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