A sequence is defined by s_n=(s_{n-1}-1)(s_{n-2}) for n 2, and it ha

Question

A sequence is defined by  s_n=(s_{n-1}-1)(s_{n-2})  for n > 2, and it has the starting values of  s_1=2  and  s_2=3 . Find the value of  s_6 .

A. 25 
B. 32 
C. 36 
D. 93 
E. 279

Kudos for a correct  solution .

mehrdadtaheri92 · Answer

Answer is E

we are given the pattern in which each term in the sequence could find by using the previous and the term before the previous term in the sequence.

so, for instance to find s3 we need to know s2 and also s1 . we are given s1 = 2 and s2 = 3 and we are ask to find s6 , so in order to calculate s6 , we need to know s5 as well as s4 and in the same way we need to know s3 to find s5 and s4 too.

so ,lets find s3 at the first step. we have a formula : s3 = (sn-1 -1 ) * ( sn-2) here : sn-1 for n=3 is s2 and sn-2 for n=3 is s1

so , we have : s3= ( s2-1) * (s1) = ( 3-1) *( 2 ) = 2*2=4

in the same way to find s4 we need to know s3 and s2 . so, we have : s4 = ( s3-1) * ( s2) = ( 4-1) * ( 3) = 3*3=9

For s5 : s5= (s4-1) * ( s3) = (9-1) *(4) = 8*4=32

And FINALLY: s6 = ( s5-1) *(s4) = (32-1) *(9) =31*9 =279 answer : E

With the best regards,

Bunuel · Answer

MAGOOSH OFFICIAL SOLUTION: This is a recursive sequence, and we have to find it term by term. gpp-s_img11.png Answer = (E).

funnypanks · Answer

I just came across this question on Magoosh, but instead of giving s1 and s2, they gave s1 and s4. 
s1=2
s4=9
All other details are identical.

How would you solve this now?

Kudos for correct response!

SeanWtx · Answer

I saw this variation as well, and was initially completely lost, but if you can assume that each term is a positive integer, you could also assume that for s4 to equal 9, it's likely it equals 9 because 3 was multiplied by 3. The only other option would be 9 * 1 which we can rule out because the sequence only increases in value, and s1 = 2 & s4 = 9, so s2 or s3 cannot = 1 or 9.

So now that we know the s4 equation is 3 * 3, we know s4-2 (aka s2) = 3, and s4-1 (aka s3) = 4, and we can solve the sequence as shown above for s6.

bumpbot · Answer

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A sequence is defined by s_n=(s_{n-1}-1)(s_{n-2}) for n > 2, and it ha

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