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 Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

Sequence S is defined as Sn=Sn-1 + 1 +1/(Sn-1 + 1) for all n [#permalink]

Show Tags

19 Dec 2012, 06:18

1

This post received KUDOS

10

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

75% (hard)

Question Stats:

57% (03:11) correct
43% (01:42) wrong based on 237 sessions

HideShow timer Statistics

Sequence S is defined as Sn = (Sn-1 +1) + {1 / (Sn-1 +1)} for all n > 1. If S1 = 100, then which of the following must be true of Q, the sum of the first 16 terms of S?

Official Answer and Stats are available only to registered users. Register/Login.

_________________

Don't give up on yourself ever. Period. Beat it, no one wants to be defeated (My journey from 570 to 690): http://gmatclub.com/forum/beat-it-no-one-wants-to-be-defeated-journey-570-to-149968.html

Last edited by daviesj on 19 Dec 2012, 23:09, edited 1 time in total.

Re: Sequence S is defined as for all n > 121. [#permalink]

Show Tags

19 Dec 2012, 07:49

4

This post received KUDOS

daviesj wrote:

Sequence S is defined as Sn = (Sn-1 +1) + {1 / (Sn-1 +1)} for all n > 1. If S1 = 100, then which of the following must be true of Q, the sum of the first 16 terms of S? (A) 1,600 ≤ Q ≤ 1,650 (B) 1,650 ≤ Q ≤ 1,700 (C) 1,700 ≤ Q ≤ 1,750 (D) 1,750 ≤ Q ≤ 1,800 (E) 1,800 ≤ Q ≤ 1,850

method to solve plz...

\(S_1 = 100\)

\(S_2 = \frac{101^2 + 1}{101} \approx 101\) (Since 1 is negligible when compared to \(101^2\))

So, the series is almost an arithmetic progression with a=100, d=1,

We have got to find the sum of "n" terms where "n" is 16.

\(S_{16} = \frac{16}{2}*(2*100 + (16-1)*1)\)

= 8*215 = 1720

Answer is C.
_________________

Did you find this post helpful?... Please let me know through the Kudos button.

Sequence S is defined as Sn = (Sn-1 +1) + {1 / (Sn-1 +1)} for all n > 1. If S1 = 100, then which of the following must be true of Q, the sum of the first 16 terms of S? (A) 1,600 ≤ Q ≤ 1,650 (B) 1,650 ≤ Q ≤ 1,700 (C) 1,700 ≤ Q ≤ 1,750 (D) 1,750 ≤ Q ≤ 1,800 (E) 1,800 ≤ Q ≤ 1,850

method to solve plz...

S1 has been given a big value i.e. 100 instead of the usual 0/1 etc. Why? Because 1/100 is negligible when added to 101

Re: Sequence S is defined as for all n > 121. [#permalink]

Show Tags

19 Dec 2012, 21:07

VeritasPrepKarishma wrote:

daviesj wrote:

Sequence S is defined as Sn = (Sn-1 +1) + {1 / (Sn-1 +1)} for all n > 1. If S1 = 100, then which of the following must be true of Q, the sum of the first 16 terms of S? (A) 1,600 ≤ Q ≤ 1,650 (B) 1,650 ≤ Q ≤ 1,700 (C) 1,700 ≤ Q ≤ 1,750 (D) 1,750 ≤ Q ≤ 1,800 (E) 1,800 ≤ Q ≤ 1,850

method to solve plz...

S1 has been given a big value i.e. 100 instead of the usual 0/1 etc. Why? Because 1/100 is negligible when added to 101

The sum will be a little more than 1720. Answer (c)

i would say the question is wrong or, atleast, not an exact GMAT type question...why to assume N as an integer...it is not specified in the question that n is an integer....n could be 1.2, 1.2,....etc for n>1 when n is not an integer.... i am thinking in the GMAT prospective...what is the source of this qtn?

Last edited by muralilawson on 19 Dec 2012, 21:53, edited 2 times in total.

Re: Sequence S is defined as for all n > 121. [#permalink]

Show Tags

19 Dec 2012, 21:19

1

This post was BOOKMARKED

daviesj wrote:

Sequence S is defined as Sn = (Sn-1 +1) + {1 / (Sn-1 +1)} for all n > 1. If S1 = 100, then which of the following must be true of Q, the sum of the first 16 terms of S? (A) 1,600 ≤ Q ≤ 1,650 (B) 1,650 ≤ Q ≤ 1,700 (C) 1,700 ≤ Q ≤ 1,750 (D) 1,750 ≤ Q ≤ 1,800 (E) 1,800 ≤ Q ≤ 1,850

method to solve plz...

S1 = \(100\)

S2 = \(100 + (1 + \frac{1}{101})\) If you will notice \(1 + \frac{1}{101}\) is approximately 1... S2 = 100 + 1 is approx. ~ 101

S3 = \(101 + (1 + \frac{1}{101})\) If you wil notice \(1 + \frac{1}{101}\) is approximately 1... S3 = 101 + 1 approx. ~ 102

Re: Sequence S is defined as for all n > 121. [#permalink]

Show Tags

19 Dec 2012, 21:52

muralilawson wrote:

VeritasPrepKarishma wrote:

daviesj wrote:

Sequence S is defined as Sn = (Sn-1 +1) + {1 / (Sn-1 +1)} for all n > 1. If S1 = 100, then which of the following must be true of Q, the sum of the first 16 terms of S? (A) 1,600 ≤ Q ≤ 1,650 (B) 1,650 ≤ Q ≤ 1,700 (C) 1,700 ≤ Q ≤ 1,750 (D) 1,750 ≤ Q ≤ 1,800 (E) 1,800 ≤ Q ≤ 1,850

method to solve plz...

S1 has been given a big value i.e. 100 instead of the usual 0/1 etc. Why? Because 1/100 is negligible when added to 101

The sum will be a little more than 1720. Answer (c)

i would say the question is wrong or, atleast, not an exact GMAT question...why to assume N as an integer...it is not specified in the question that n is an integer....n could be 1.2, 1.2,....etc for n>1 when n is not an integer.... i am thinking in the GMAT prospective...

Since this is a PS question and not a DS question, we are free to make that assumption. "n" is only a subscript indicating the ordinal number of each term and hence can be taken to be integers.
_________________

Did you find this post helpful?... Please let me know through the Kudos button.

Re: Sequence S is defined as Sn=Sn-1 + 1 +1/(Sn-1 + 1) for all n [#permalink]

Show Tags

28 Sep 2014, 07:38

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.
_________________

Re: Sequence S is defined as Sn=Sn-1 + 1 +1/(Sn-1 + 1) for all n [#permalink]

Show Tags

17 Oct 2015, 02:49

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.
_________________

Sequence S is defined as Sn = (Sn-1 +1) + {1 / (Sn-1 +1)} for all n > 1. If S1 = 100, then which of the following must be true of Q, the sum of the first 16 terms of S?

Its been long time coming. I have always been passionate about poetry. It’s my way of expressing my feelings and emotions. And i feel a person can convey...

Written by Scottish historian Niall Ferguson , the book is subtitled “A Financial History of the World”. There is also a long documentary of the same name that the...

Post-MBA I became very intrigued by how senior leaders navigated their career progression. It was also at this time that I realized I learned nothing about this during my...