GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 23 Feb 2020, 21:58

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

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

Author Message
TAGS:

### Hide Tags

Magoosh GMAT Instructor
Joined: 28 Dec 2011
Posts: 4476
If a sequence is defined by a_n = (a_(n-1))*(a_(n-2)) for all n >=3  [#permalink]

### Show Tags

Updated on: 23 Sep 2014, 14:05
1
2
00:00

Difficulty:

15% (low)

Question Stats:

80% (01:34) correct 20% (01:23) wrong based on 102 sessions

### HideShow timer Statistics

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:
http://magoosh.com/gmat/2012/sequences-on-the-gmat/

Mike

_________________
Mike McGarry
Magoosh Test Prep

Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)

Originally posted by mikemcgarry on 23 Sep 2014, 09:26.
Last edited by mikemcgarry on 23 Sep 2014, 14:05, edited 1 time in total.
GMAT Tutor
Joined: 24 Jun 2008
Posts: 2012
Re: If a sequence is defined by a_n = (a_(n-1))*(a_(n-2)) for all n >=3  [#permalink]

### Show Tags

23 Sep 2014, 12:22
1
mikemcgarry wrote:
[color=#0000ff]If a sequence is defined by $$a_n = (a_{n-1})*(a_{n-2})$$ for all $$n\geq3$$, and if $$a_1 = 1$$ and $$a_2 = 1$$, what is the 6th term?

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 $$n\geq3$$
_________________
GMAT Tutor in Montreal

If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com
SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1713
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: If a sequence is defined by a_n = (a_(n-1))*(a_(n-2)) for all n >=3  [#permalink]

### Show Tags

01 Oct 2014, 00:34
1
$$a_1 = 1$$

$$a_2 = 1$$

$$a_3 = 1 * 1 + 1 = 2$$

$$a_4 = 2*1+1 = 3$$

$$a_5 = 3*2 + 1 = 7$$

$$a_6 = 7*3 + 1 = 22$$

Magoosh GMAT Instructor
Joined: 28 Dec 2011
Posts: 4476
Re: If a sequence is defined by a_n = (a_(n-1))*(a_(n-2)) for all n >=3  [#permalink]

### Show Tags

23 Sep 2014, 14:06
IanStewart wrote:
mikemcgarry wrote:
[color=#0000ff]If a sequence is defined by $$a_n = (a_{n-1})*(a_{n-2})$$ for all $$n\geq3$$, and if $$a_1 = 1$$ and $$a_2 = 1$$, what is the 6th term?

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 $$n\geq3$$

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
_________________
Mike McGarry
Magoosh Test Prep

Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)
EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 16141
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: If a sequence is defined by a_n = (a_(n-1))*(a_(n-2)) for all n >=3  [#permalink]

### Show Tags

08 Dec 2019, 14:43
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

GMAT assassins aren't born, they're made,
Rich
_________________
Contact Rich at: Rich.C@empowergmat.com

The Course Used By GMAT Club Moderators To Earn 750+

souvik101990 Score: 760 Q50 V42 ★★★★★
ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★
Re: If a sequence is defined by a_n = (a_(n-1))*(a_(n-2)) for all n >=3   [#permalink] 08 Dec 2019, 14:43
Display posts from previous: Sort by