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For a certain sequence, tn=-1(tn-1+1)^-1 for all values of n [#permalink]

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02 Nov 2005, 18:01

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For a certain sequence, tn=-1(tn-1+1)^-1 for all values of n such that n => 2. Given that t1=1, how much greater is the product of the first 200 values in this sequence than the sum of the first 200 values in this sequence?

1
68
98
105
228

Give it a
_________________

"Wow! Brazil is big." â€”George W. Bush, after being shown a map of Brazil by Brazilian president Luiz Inacio Lula da Silva, Brasilia, Brazil, Nov. 6, 2005

For a certain sequence, tn=-1(tn-1+1)^-1 for all values of n such that n >= 2 Given that t1=1, how much greater is the product of the first 200 values in this sequence than the sum of the first 200 values in this sequence?

1 68 98 105 228

Give it a

from the formula we can calculate
t2= -1/2 , t3=-2, t4= 1 , t5=-1/2 , t6=-2, t7= 1, this repeats over and over with interval of 3
the sum is t2+ t3+ t4+ ... + t200 = ( t2+t3+t4) + ( t5+t6+t7) + ....+ (t197+t198+t199)+t200
Each sum in the ( ) has the value of -1/2+(-2)+1= -3/2
We have 66 groups in all --> the sum except for t200 is -3/2*66= -99
---> the whole sum is -99+t200= -99-1/2= -99.5

The product of t2*t3*t4= -1/2*-2* 1= 1
We have 66 such groups in all --> the product of these 66 groups is 1
--> the product of these 66 groups with t200= 1*(-1/2) = -1/2
---> the product- the sum= -1/2 -(-99.5) = 99

The slight difference is because I assumed that n>=2 ...coz if we don't have n=2, we can't never calculate t2 and thus t3,t4,t5 ......

Last edited by laxieqv on 02 Nov 2005, 22:00, edited 1 time in total.

where is our frens lexieqv,qsr,himalaya,gmatt73..??? any hint titleist?

yeah where is everyone?

as for the hint. find the pattern for the first 10 terms. you'll be able to find a pattern once you sum vs. mulitplying.
_________________

"Wow! Brazil is big." â€”George W. Bush, after being shown a map of Brazil by Brazilian president Luiz Inacio Lula da Silva, Brasilia, Brazil, Nov. 6, 2005

hey, are you sure n > 2 ... I think it should be n > =2

good find yes - let me make the edit.
_________________

"Wow! Brazil is big." â€”George W. Bush, after being shown a map of Brazil by Brazilian president Luiz Inacio Lula da Silva, Brasilia, Brazil, Nov. 6, 2005

The sum of of the sequence for the first 3 terms is -1.5 and it is -1.5 for every subsequent 3 terms.

The product of the three terms is 1 and repeats itself every three terms.

If we take 200 terms and divided by the number of cycles, 3, then we get 66. However 66 x 3 is 198 thus we have to add or multiply the 199th and 200th terms.

The product 1^66 = 1 x 1 (199th term) x -0.5 (200th term) = -0.5 (is the product of the first 200 terms of the sequence

The sum -1.5 x 66 = -99 + 1 (199 term) + -0.5 (200th term) = -98.5

The product - The sum = -0.5 - (-98.5) = 98
_________________

"Wow! Brazil is big." â€”George W. Bush, after being shown a map of Brazil by Brazilian president Luiz Inacio Lula da Silva, Brasilia, Brazil, Nov. 6, 2005

hey, are you sure n > 2 ... I think it should be n > =2

good find yes - let me make the edit.

hey..you made me stare at this problem from last 1 hour... to find elusive t2 while only thing we can know is t1 and t3,t4,...

be back from the break

SORRRY!!!!
_________________

"Wow! Brazil is big." â€”George W. Bush, after being shown a map of Brazil by Brazilian president Luiz Inacio Lula da Silva, Brasilia, Brazil, Nov. 6, 2005

well, please see my solution which is right above your last

If we take 200 terms and divided by the number of cycles, 3, then we get 66. However 66 x 3 is 198 thus we have to add or multiply the 199th and 200th terms.

Hey ,aren't we considering n from 2 to 200???? there are 200-2+1= 199 numbers in the set! and thus 66 groups and only t200 left!

well, please see my solution which is right above your last

If we take 200 terms and divided by the number of cycles, 3, then we get 66. However 66 x 3 is 198 thus we have to add or multiply the 199th and 200th terms.

Hey, aren't we considering n from 2 to 200???? there are 200-2+1= 199 numbers in the set! and thus 66 groups and only t200 left!

No - I think the question explicitly asks for the first 200 values not just 199 values, so you would have to start from T1. The question tells you that n=>2 because they are giving you a starting point from which you can derive the sequence from T1. OA from Manhattan Gmat stands at 98. I double checked the question.
_________________

"Wow! Brazil is big." â€”George W. Bush, after being shown a map of Brazil by Brazilian president Luiz Inacio Lula da Silva, Brasilia, Brazil, Nov. 6, 2005

well, please see my solution which is right above your last

If we take 200 terms and divided by the number of cycles, 3, then we get 66. However 66 x 3 is 198 thus we have to add or multiply the 199th and 200th terms.

Hey, aren't we considering n from 2 to 200???? there are 200-2+1= 199 numbers in the set! and thus 66 groups and only t200 left!

No - I think the question explicitly asks for the first 200 values not just 199 values, so you would have to start from T1. The question tells you that n=>2 because they are giving you a starting point from which you can derive the sequence from T1. OA from Manhattan Gmat stands at 98. I double checked the question.

ok, i accept that ...anyway this one is not tough but tricky ...and it's EXTREMELY tricker as you omitted n=2

well, please see my solution which is right above your last

If we take 200 terms and divided by the number of cycles, 3, then we get 66. However 66 x 3 is 198 thus we have to add or multiply the 199th and 200th terms.

Hey, aren't we considering n from 2 to 200???? there are 200-2+1= 199 numbers in the set! and thus 66 groups and only t200 left!

No - I think the question explicitly asks for the first 200 values not just 199 values, so you would have to start from T1. The question tells you that n=>2 because they are giving you a starting point from which you can derive the sequence from T1. OA from Manhattan Gmat stands at 98. I double checked the question.

ok, i accept that ...anyway this one is not tough but tricky ...and it's EXTREMELY tricker as you omitted n=2

Ok Ok! I'm sorry about that - I assure you that there was no malice involved - it was just an innocent mistake!

_________________

"Wow! Brazil is big." â€”George W. Bush, after being shown a map of Brazil by Brazilian president Luiz Inacio Lula da Silva, Brasilia, Brazil, Nov. 6, 2005

Laxi, try the Honey Bee probability question - you'll enjoy that one.
_________________

"Wow! Brazil is big." â€”George W. Bush, after being shown a map of Brazil by Brazilian president Luiz Inacio Lula da Silva, Brasilia, Brazil, Nov. 6, 2005

oh my ....your that emoticon tells thousands of words ...btw, it's great fun to have you playing some jokes around ..But for this thread, I stop chit-chatting, if not I'm gonna get "fired" by CEO

oh my ....your that emoticon tells thousands of words ...btw, it's great fun to have you playing some jokes around ..But for this thread, I stop chit-chatting, if not I'm gonna get "fired" by CEO

Fired? He'd better give you a nice severance package Laxieqv.
_________________

"Wow! Brazil is big." â€”George W. Bush, after being shown a map of Brazil by Brazilian president Luiz Inacio Lula da Silva, Brasilia, Brazil, Nov. 6, 2005