If a sequence is defined by

[VJesus12]

If a sequence is defined by \(a_n=(a_n−1)\cdot(a_n−2)+1\) for all \(n ≥ 3\), and if \(a_1=1\) and \(a_2=1\), what is the 6th term?
(A) 1
(B) 7
(C) 22
(D) 155
(E) 721

[spoiler]OA=C[/spoiler]

Source: Magoosh

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Hi All,

To start, there's a slight 'formatting' issue with the original question. The proper interpretation of the question is explained below.

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

[Scott@TargetTestPrep]

If a sequence is defined by \(a_n=(a_n−1)\cdot(a_n−2)+1\) for all \(n ≥ 3\), and if \(a_1=1\) and \(a_2=1\), what is the 6th term?
(A) 1
(B) 7
(C) 22
(D) 155
(E) 721

[spoiler]OA=C[/spoiler]

Source: Magoosh

(Note the notation error in the question stem. The sequence definition should read
a(n) = [a(n-1) x a(n-2)] + 1.)

a(3) = 1 x 1 + 1 = 2

a(4) = 2 x 1 + 1 = 3

a(5) = 3 x 2 + 1 = 7

a(6) = 7 x 3 + 1 = 22

Answer: C