BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

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

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Senior | Next Rank: 100 Posts
Posts: 52
Joined: Sat Aug 13, 2011 8:34 am
Thanked: 2 times

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

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
Top
Source: — Problem Solving |
Legendary Member
Posts: 1448
Joined: Tue May 17, 2011 9:55 am
Location: India
Thanked: 375 times
Followed by:53 members

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
Top
User avatar
Master | Next Rank: 500 Posts
Posts: 312
Joined: Tue Aug 02, 2011 3:16 pm
Location: New York City
Thanked: 130 times
Followed by:33 members
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.
Top
Legendary Member
Posts: 2789
Joined: Tue Jul 26, 2011 12:19 am
Location: Chennai, India
Thanked: 206 times
Followed by:43 members
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
Top
Post new topic Post Reply
• Page 1 of 1