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sequence series.

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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.
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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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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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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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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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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.
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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.
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Let me know if you have any doubt.
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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.
Image

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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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.
Image

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 ,
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