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:

0% (00:00) correct 0% (00:00) wrong based on 0 sessions

HideShow timer Statistics

This topic is locked. If you want to discuss this question please re-post it in the respective forum.

Hey, here's another one from the gmat prep. I do not understand the question. Please help!

For every integer k from 1 to 10 inclusive, the kth term of a certain sequence is given by (-1)^(k+1) (1/2^k). If T is the sum of the first 10 terms, what is the value range for T?

note: -1 is raised to k+1, and the 2 of 1/2 is raised k

k = 1 to 10
So,
1st term of the series = (-1)^2 x (1/2) = 1/2
2nd term of the series = (-1)^3 x (1/4) = -1/4
3rd term of the series = (-1)^4 x (1/8) = 1/8

Hence, common ratio r = -1/2 --> Geometric series
T is the sum of k terms and r < 1, so:
T = a[(1-r^k)/(1-r)] = 0.5[(1-(-0.5)^10)/91+0.5)] = 1023/(1024*3)
T ~= 1/3
_________________

1/3 is between 1/4 and 1/2.
I vaguely remember this question and from the answer choices, I think the only one that accomodates 1/3 is "between 1/4 and 1/2".

Guys, the question asks for the value range for T.

This confused me at the start ..... value range = sum ??!?! I wouldve just calculated the first term and the tenth term, and then subtracted the two to find the 'value range' ....

How in the world do you guys figure this out? Can some one please explain this...

Hence, common ratio r = -1/2 --> Geometric series
T is the sum of k terms and r < 1, so:
T = a[(1-r^k)/(1-r)] = 0.5[(1-(-0.5)^10)/91+0.5)] = 1023/(1024*3)
T ~= 1/3

If the terms in a series have a common ratio, its a geometric series and there are generalised formulae for working out the nth term of the series and the sum of n terms.

If the terms have a common difference its an arithmetic series and again there are formulae for the nth term and sum of n terms.

So in the question above, I've worked out the common ratio (from the terms) and then used the formula for sum to get the value for T.

How in the world do you guys figure this out? Can some one please explain this...

Hence, common ratio r = -1/2 --> Geometric series T is the sum of k terms and r < 1, so: T = a[(1-r^k)/(1-r)] = 0.5[(1-(-0.5)^10)/91+0.5)] = 1023/(1024*3) T ~= 1/3

Thanks!

Can someone please explain the part highlighted.

where did 91 come from , should (1-r) = 1 - (-0.5)
I know I am missing an important point here.