Series Qn MGMAT Any faster way to do this, and key message?

Expert replies

kaps786: Senior | Next Rank: 100 Posts; Posts: 52; Joined: Sat Aug 13, 2011 8:34 am; Thanked: 2 times

by kaps786 » Sat Aug 13, 2011 9:06 am

Experts

Is there any faster way to do this, sequences question - instead of calculating each and every term until S10, which was taking forever.

Lastly, is this typical of GMAT?, what is being tested here or key message to keep in mind, for such questions. It took me few seconds to even get started.

Sequence S is defined as Sn = 2Sn-1 - 2. If S1 = 3, then S10 - S9 =

2
120
128
250
256

OA E

Thanks
Kaps

Like this post

Source: Beat The GMAT — Problem Solving | Sat Aug 13, 2011 9:06 am

Frankenstein: Legendary Member; Posts: 1448; Joined: Tue May 17, 2011 9:55 amFollowed by: 53 members; Location: India; Thanked: 375 times

by Frankenstein » Sat Aug 13, 2011 9:31 am

Hi,
Faster method would be trying to find the pattern.
Sn is 2 times the previous term and then subtracted by some constant.
So, Sn should be having a 2^n since a2^n = a.2.2^(n-1), where 'a' is a constant.
So, once we realize this we can find other things as well.
In this case Sn = a2^n + 2
For n=1, S1 = a.2^(1) + 2 = 3. So, 2a = 1 =>a=1/2
So, Sn = 2^(n-1) + 2
S10 = 2^9 + 2
S9 = 2^8 + 2
So, S10-S9 = 2^9 - 2^8 = 512-256 = 256.

In a similar way, If Sn = 3Sn-1 + constant when Sn will be of the form Sn = a.3^n + b.

Cheers!

Things are not what they appear to be... nor are they otherwise

Like this post

gmatboost: Master | Next Rank: 500 Posts; Posts: 312; Joined: Tue Aug 02, 2011 3:16 pmFollowed by: 33 members; Location: New York City; Thanked: 130 times; GMAT Score:780

by gmatboost » Mon Aug 15, 2011 9:24 am

My approach was to write out the first few and look for a pattern in the differences, since the question asks for S10 - S9.

The first few are 3, 4, 6, 10, 18.
Differences: 1, 2, 4, 8 ... (powers of 2)

Greg Michnikov, Founder of GMAT Boost

GMAT Boost offers 250+ challenging GMAT Math practice questions, each with a thorough video explanation, and 100+ GMAT Math video tips, each 90 seconds or less.
It's a total of 20+ hours of expert instruction for an introductory price of just $10.
View sample questions and tips without signing up, or sign up now for full access.

Also, check out the most useful GMAT Math blog on the internet here.

Like this post

GmatKiss: Legendary Member; Posts: 2789; Joined: Tue Jul 26, 2011 12:19 amFollowed by: 43 members; Location: Chennai, India; Thanked: 206 times; GMAT Score:640

by GmatKiss » Mon Aug 15, 2011 10:22 pm

I feel the link below has a wonderful explanation to this problem!

https://www.beatthegmat.com/sequences-t9560.html#38369

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

559 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (560 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review