For each positive integer,the quantitySn is defined such thatSn+2=(Sn)^2 -S(n+2).in addition ,S2=1.then which of the following must be true.
Pick: A) a)S4 +S3 +1=0 B) b)(S1)^2 +S4 +2=0 C) c) ifS1=-1thenS4 is also equal to-1. D) d) ifS4 =-7thenS1=-2. E) e) ifS1 =-3thenS4=-7
Since all the answers include S4, let's start from there.   S4=S2^2-S3   S3=S1^2-S2   Substituting S3 into the first equation we get:   S4=S2^2-(S1^2-S2)   Since S2=1   S4=1-(S1^2-1)   S4=2-S1^2   We need S1^2 in order to calculate S4.   E) provides S1 and from there we can calculate S4:   S4=2-(-3)^2   S4=-7   Correct.   As a side note, I would be very careful with answers in the formif S4=x then S1=y(such as option D ), as we are dealing with S1^2 (not S1), S1 can have two different values and it can not be determined for sure which root is the right answer.   For example:   If S4=-7 then S1=3 :   if we substitute S4 with - 7 we get:   -7=2-S1^2   S1^2=9   now S1 can be +/-3 !!   e) ifS1 =-3thenS4=-7
<result>E</result>
For each positive integer,the quantitySn is defined such thatSn+2=(Sn)^2 -S(n+2).in addition ,S2=1.then which of the following must be true.