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

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kaps786: 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

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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 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

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gmatboost: 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)

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