sequence series.

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goyalsau: Legendary Member; Posts: 866; Joined: Mon Aug 02, 2010 6:46 pm; Location: Gwalior, India; Thanked: 31 times

by goyalsau » Sun Dec 05, 2010 3:46 am

There is a sequence of numbers whose nth term is tn. It is given that Tn = ( (Tn - 1) - 1)^2 + 1, where n is a positive integer greater than 1. If T1 = 3, what is the product of the first 10 terms of the sequence?

(Tn - 1)- Previous Term from Tn

(2^1023) - 1

(2^1024) - 1

(2^512) - 1

(2^2048) - 1

(2^1025) - 1

Last edited by goyalsau on Sun Dec 05, 2010 5:39 pm, edited 1 time in total.

Saurabh Goyal
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Source: Beat The GMAT — Problem Solving | Sun Dec 05, 2010 3:46 am

beat_gmat_09: Master | Next Rank: 500 Posts; Posts: 437; Joined: Sat Nov 22, 2008 5:06 amFollowed by: 1 member; Location: India; Thanked: 50 times; GMAT Score:580

by beat_gmat_09 » Sun Dec 05, 2010 10:17 am

Whats the source of this question ?
looks as if this needs applying binomial theorem or something !

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oddball: Junior | Next Rank: 30 Posts; Posts: 11; Joined: Fri Oct 29, 2010 3:25 am

by oddball » Sun Dec 05, 2010 10:23 am

I think there is some problem with the question or options. Here is how I approached...

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goyalsau: Legendary Member; Posts: 866; Joined: Mon Aug 02, 2010 6:46 pm; Location: Gwalior, India; Thanked: 31 times

by goyalsau » Sun Dec 05, 2010 11:05 am

This is the solution , that they provided, But i am not able to understand How they solve the Equation......

Once they reach the value of T10 = 2^512 + 1

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Saurabh Goyal
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oddball: Junior | Next Rank: 30 Posts; Posts: 11; Joined: Fri Oct 29, 2010 3:25 am

by oddball » Sun Dec 05, 2010 11:10 am

goyalsau wrote:There is a sequence of numbers whose nth term is tn. It is given that Tn = ( (Tn - 1) - 1)2 + 1, where n is a positive integer greater than 1. If T1 = 3, what is the product of the first 10 terms of the sequence?

You provided wrong question dude!

In the solution you provided 2 is the power of T(n-1), not multiplied with it!

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goyalsau: Legendary Member; Posts: 866; Joined: Mon Aug 02, 2010 6:46 pm; Location: Gwalior, India; Thanked: 31 times

by goyalsau » Sun Dec 05, 2010 5:40 pm

oddball wrote:
goyalsau wrote:There is a sequence of numbers whose nth term is tn. It is given that Tn = ( (Tn - 1) - 1)2 + 1, where n is a positive integer greater than 1. If T1 = 3, what is the product of the first 10 terms of the sequence?
You provided wrong question dude!

In the solution you provided 2 is the power of T(n-1), not multiplied with it!

Thanks Buddy, I edited the question.

Saurabh Goyal
[email protected]
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EveryBody Wants to Win But Nobody wants to prepare for Win.

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Rahul@gurome: GMAT Instructor; Posts: 1179; Joined: Sun Apr 11, 2010 9:07 pmFollowed by: 88 members; Location: Milpitas, CA; Thanked: 447 times

by Rahul@gurome » Mon Dec 06, 2010 3:49 am

goyalsau wrote:There is a sequence of numbers whose nth term is tn. It is given that Tn = ( (Tn - 1) - 1)^2 + 1, where n is a positive integer greater than 1. If T1 = 3, what is the product of the first 10 terms of the sequence?

(Tn - 1)- Previous Term from Tn

Here is the solution. The approach is same as the provided solution. But I tried to give a detailed explanation.

Let me know if you have any doubt.

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diebeatsthegmat: Legendary Member; Posts: 1119; Joined: Fri May 07, 2010 8:50 amFollowed by: 3 members; Thanked: 29 times

by diebeatsthegmat » Mon Dec 06, 2010 11:51 am

Rahul@gurome wrote:
goyalsau wrote:There is a sequence of numbers whose nth term is tn. It is given that Tn = ( (Tn - 1) - 1)^2 + 1, where n is a positive integer greater than 1. If T1 = 3, what is the product of the first 10 terms of the sequence?

(Tn - 1)- Previous Term from Tn
Here is the solution. The approach is same as the provided solution. But I tried to give a detailed explanation.

Let me know if you have any doubt.

yes, i did the same but its so time consuming.... hey rahul, do you think this kind of time-consuming math will be on test???

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goyalsau: Legendary Member; Posts: 866; Joined: Mon Aug 02, 2010 6:46 pm; Location: Gwalior, India; Thanked: 31 times

by goyalsau » Mon Dec 06, 2010 7:14 pm

diebeatsthegmat wrote:
Rahul@gurome wrote:
goyalsau wrote:There is a sequence of numbers whose nth term is tn. It is given that Tn = ( (Tn - 1) - 1)^2 + 1, where n is a positive integer greater than 1. If T1 = 3, what is the product of the first 10 terms of the sequence?

(Tn - 1)- Previous Term from Tn
Here is the solution. The approach is same as the provided solution. But I tried to give a detailed explanation.

Let me know if you have any doubt.
yes, i did the same but its so time consuming.... hey rahul, do you think this kind of time-consuming math will be on test???

Gmat is a adaptive test, Once your perform good on the test, Question will be harder,

According to me Definition of Difficult problem is not that they are difficult. It is that we are not much familiar with the concept, Because This problem could have been solved in less than 2 minutes If one can realize the trick of 2^1 - 1 ,

Saurabh Goyal
[email protected]
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EveryBody Wants to Win But Nobody wants to prepare for Win.

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