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:

In the sequence of nonzero numbers t1, t2, t3, , tn, , tn+1 [#permalink]

Show Tags

18 Jun 2008, 09:23

6

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

35% (medium)

Question Stats:

65% (02:13) correct
35% (01:27) wrong based on 314 sessions

HideShow timer Statistics

In the sequence of nonzero numbers \(t_1\), \(t_2\), \(t_3\), …, \(t_n\), …, \(t_{n+1}=\frac{t_n}{2}\) for all positive integers n. What is the value of \(t_5\)?

Re: In the sequence of nonzero numbers t1, t2, t3, , tn, , tn+1 [#permalink]

Show Tags

18 Jun 2008, 11:11

1

This post received KUDOS

Hello, quantum, this is my attempt to explain why it's D:

Quote:

In the sequence of nonzero numbers t1, t2, t3, …, tn, …, tn+1 = tn / 2 for all positive integers n. What is the value of t5? (1) t3 = 1/4 (2) t1 - t5 = 15/16

Here we have geometric progression, i.e. series where t2=t1*q, t3=t2*q, …, tn+1=tn*q. In our case, q=0.5. Also note that tn+1=t1*q^n

So, basically, to answer this question, it is sufficient to know the value of any of the tn.

1) Explicitly gives us the value for t3, so it’s sufficient.

2) So, let’s see if we can obtain the value of t1 from this statement, using the formula tn+1=t1*q^n:

Re: In the sequence of nonzero numbers t1, t2, t3, , tn, , tn+1 [#permalink]

Show Tags

18 Jun 2008, 12:43

7

This post received KUDOS

1

This post was BOOKMARKED

quantum wrote:

In the sequence of nonzero numbers t1, t2, t3, …, tn, …, tn+1 = tn / 2 for all positive integers n. What is the value of t5? (1) t3 = 1/4 (2) t1 - t5 = 15/16

see attached

Attachments

sequence.gif [ 6.83 KiB | Viewed 11756 times ]

_________________

Factorials were someone's attempt to make math look exciting!!!

Re: In the sequence of nonzero numbers t1, t2, t3, , tn, , tn+1 [#permalink]

Show Tags

19 Dec 2010, 15:31

Good explanations but I got confused at how you equated tn+1=tn/2? I thought the it was the entire expression that equaled to tn/2? sorry but I am a bit confused. Thanks.

Good explanations but I got confused at how you equated tn+1=tn/2? I thought the it was the entire expression that equaled to tn/2? sorry but I am a bit confused. Thanks.

In the sequence of nonzero numbers t1, t2, t3, …, tn, …, tn+1 = tn / 2 for all positive integers n. What is the value of t5?

Given: \(t_{n+1}=\frac{t_n}{2}\). So \(t_2=\frac{t_1}{2}\), \(t_3=\frac{t_2}{2}=\frac{t_1}{4}\), \(t_4=\frac{t_3}{2}=\frac{t_1}{8}\), ...

Basically we have geometric progression with common ratio \(\frac{1}{2}\): \(t_1\), \(\frac{t_1}{2}\), \(\frac{t_1}{4}\), \(\frac{t_1}{8}\), ... --> \(t_n=\frac{t_1}{2^{n-1}}\).

Question: \(t_5=\frac{t_1}{2^4}=?\)

(1) \(t_3=\frac{1}{4}\) --> we can get \(t_1\) --> we can get \(t_5\). Sufficient. (2) \(t_1-t_5=2^4*t_5-t_5=\frac{15}{16}\) --> we can get \(t_5\). Sufficient.

Answer: D.

Generally for arithmetic (or geometric) progression if you know:

- any particular two terms, - any particular term and common difference (common ratio), - the sum of the sequence and either any term or common difference (common ratio),

then you will be able to calculate any missing value of given sequence.

Re: In the sequence of nonzero numbers t1, t2, t3, , tn, , tn+1 [#permalink]

Show Tags

15 Apr 2014, 01:43

1

This post received KUDOS

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: In the sequence of nonzero numbers t1, t2, t3, , tn, , tn+1 [#permalink]

Show Tags

22 Nov 2014, 09:31

Bunuel. I have a question about the 3rd generalized case. What does 'the formula for nth term' mean? Is it a+(n-1)d? I am guessing not since (a)we already know that as a formula and (b)Along with any particular term, the formula would still leave 2 variables- a and d. So are we talking about another equation for a term? Thanks again

Bunuel. I have a question about the 3rd generalized case. What does 'the formula for nth term' mean? Is it a+(n-1)d? I am guessing not since (a)we already know that as a formula and (b)Along with any particular term, the formula would still leave 2 variables- a and d. So are we talking about another equation for a term? Thanks again

You are right. I phrased that ambiguously. Will edit.
_________________

Re: In the sequence of nonzero numbers t1, t2, t3, , tn, , tn+1 [#permalink]

Show Tags

11 Jul 2016, 06:56

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.
_________________

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...