Check GMAT Club Decision Tracker for the Latest School Decision Releases https://gmatclub.com/AppTrack
GMAT Club

 It is currently 29 Mar 2017, 16:00

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# In the infinite sequence A, An = X^(n-1) + X^n + X^(n+1) + X

Author Message
TAGS:

### Hide Tags

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 14559
Followers: 609

Kudos [?]: 175 [0], given: 0

Re: In the infinite sequence A, An = X^(n-1) + X^n + X^(n+1) + X [#permalink]

### Show Tags

19 Sep 2013, 01:09
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Current Student
Joined: 17 Sep 2013
Posts: 24
Location: United States
Concentration: Economics, Statistics
Schools: CBS '18 (M)
GMAT 1: 770 Q51 V45
GPA: 3.36
WE: Analyst (Health Care)
Followers: 0

Kudos [?]: 13 [0], given: 1

Re: In the infinite sequence A, An = X^(n-1) + X^n + X^(n+1) + X [#permalink]

### Show Tags

19 Sep 2013, 13:34
Could someone please explain to me how that's an infinite sequence? That's what really threw me off.
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7256
Location: Pune, India
Followers: 2205

Kudos [?]: 14372 [0], given: 222

Re: In the infinite sequence A, An = X^(n-1) + X^n + X^(n+1) + X [#permalink]

### Show Tags

19 Sep 2013, 21:48
mfabros wrote:
Could someone please explain to me how that's an infinite sequence? That's what really threw me off.

The information that it is an infinite sequence doesn't have much to do with the question. You are given this only to tell you that n can take any positive integer value.

An = X^(n-1) + X^n + X^(n+1) + X^(n+2) + X^(n+3) tells you that the nth term is given by plugging in the value of n in this expression. A is not a sequence of 2 or 4 terms but infinite so n can take any value. We found out that the required relation holds when n is 7. We could have just as well got n = 10298 and that would have been fine too since A has infinite terms so any value for n is alright.
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for \$199

Veritas Prep Reviews

Intern
Joined: 27 Aug 2014
Posts: 1
Schools: Haas '17
Followers: 0

Kudos [?]: 0 [0], given: 8

Re: In the infinite sequence A, An = X^(n-1) + X^n + X^(n+1) + X [#permalink]

### Show Tags

13 Sep 2014, 09:18
FYI guys, this is a Manhattan Review Turbocharge question.
Manager
Joined: 14 Sep 2014
Posts: 94
WE: Engineering (Consulting)
Followers: 1

Kudos [?]: 29 [0], given: 51

Re: In the infinite sequence A, An = X^(n-1) + X^n + X^(n+1) + X [#permalink]

### Show Tags

10 Oct 2014, 03:26
It is actually very easy
Expand Brackets
we need An/(x+...+x^5) = x^5
An = x^5 (x+...+x^5)
An = x^6+....+x^10
only n = 7 satisfies..
Intern
Joined: 27 Apr 2014
Posts: 3
Followers: 0

Kudos [?]: 1 [0], given: 0

Re: In the infinite sequence A, An = X^(n-1) + X^n + X^(n+1) + X [#permalink]

### Show Tags

15 Jun 2015, 14:15
I have solved it in this way:

The question asks to find n where
An/x(1+x(1+x(1+x(1+x)))) = x^5 (1)

Factorizing An= x^(n-2)(x(1+x(1+x(1+x(1+x)))) (2)

Replacing (2) in (1) we get: X^(n-2)=x^5-->X^n=x^7-->n=7

regards
Intern
Joined: 01 Jun 2016
Posts: 1
Followers: 0

Kudos [?]: 0 [0], given: 3

Re: In the infinite sequence A, An = X^(n-1) + X^n + X^(n+1) + X [#permalink]

### Show Tags

05 Jun 2016, 19:34
A different approach...

The maximum power of "x" in the denominator is 5 because "x" appears 5 times. For the ratio to be x^5, the numerator should have x^10. The highest power of "x" in the numerator is 10; so by comparison, n+3=10 => n = 7.
Re: In the infinite sequence A, An = X^(n-1) + X^n + X^(n+1) + X   [#permalink] 05 Jun 2016, 19:34

Go to page   Previous    1   2   [ 27 posts ]

Similar topics Replies Last post
Similar
Topics:
4 For every positive integer n, if the nth term of the sequence is xN 4 28 Sep 2016, 09:28
4 If x not equal to 0, then (1/x)^n - (1/x)^(n+1) 5 10 Jun 2016, 04:50
3 X1=1, for all positive integers, Xn=1+7Xn-1 , what is the units digit 4 08 Feb 2016, 18:45
1 The sequence x1, x2, x3,..., is such that Xn = 1/n - 1/(n+1) 2 22 Sep 2012, 10:19
2 In a certain sequence, the term x_n is given by the formula 9 20 Dec 2009, 11:58
Display posts from previous: Sort by