If a sequence is defined by a_n = (a_(n-1))*(a_(n-2)) for all n =3

Question

If a sequence is defined by a_n = (a_{n-1})*(a_{n-2})+1 for all n\geq3 , and if a_1 = 1 and a_2 = 1 , what is the 6th term? (A) 1 (B) 7 (C) 22 (D) 155 (E) 721 For a discussion of questions involving sequences , especially recursive sequences such as this one, as well as the OE for this question, please see: https://magoosh.com/gmat/2012/sequences-on-the-gmat/ Mike :-)

IanStewart · Answer

As the question is written, the answer would be 1 (every term would be 1). If the correct answer is to be C here, I think you want the definition of the later terms to include a '+1' at the end:

a_n = (a_{n-1})*(a_{n-2})   + 1  for all  n\geq3

mikemcgarry · Answer

Ian, Many thanks, my friend, for catching that typo. Yes, you are 100% correct: with the "+ 1," the sequence would be utterly trivial. I corrected it the original question. Thanks again! Mike :-)

PareshGmat · Answer

a_1 = 1

a_2 = 1

a_3 = 1 * 1 + 1 = 2

a_4 = 2*1+1 = 3

a_5 = 3*2 + 1 = 7

a_6 = 7*3 + 1 = 22

Answer = C

EMPOWERgmatRichC · Answer

Hi All,

While this question might appear a bit 'scary', it's just a Sequence question and we're told exactly how the sequence 'works.' We're given the first two terms of the sequence and then told that each term that follows the first two is the (PRODUCT of the prior two terms that come before it in the sequence) plus 1. We're asked for the value of the 6th term. In these types of questions, it's usually fairly easy (and necessary) to calculate all of the terms in the sequence.

1st = 1 
2nd = 1 
3rd = (2nd term)(1st term) + 1 = (1)(1) + 1 = 2 
4th = (3rd term)(2nd term) + 1 = (2)(1) + 1 = 3 
5th = (4th term)(3rd term) + 1 = (3)(2) + 1 = 7 
6th = (5th term)(4th term) + 1 = (7)(3) + 1 = 22

Final Answer:  C

GMAT assassins aren't born, they're made, 
Rich

If a sequence is defined by a_n = (a_(n-1))*(a_(n-2)) for all n >=3

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