Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 25 Oct 2016, 13:31

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

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

Author Message
Director
Joined: 14 Oct 2003
Posts: 587
Location: On Vacation at My Crawford, Texas Ranch
Followers: 1

Kudos [?]: 44 [0], given: 0

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

### Show Tags

02 Nov 2005, 18:01
00:00

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 0 sessions

### HideShow timer Statistics

This topic is locked. If you want to discuss this question please re-post it in the respective forum.

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

http://www.nytimes.com/2005/11/21/international/asia/21prexy.html

Last edited by Titleist on 02 Nov 2005, 22:03, edited 1 time in total.
VP
Joined: 22 Aug 2005
Posts: 1120
Location: CA
Followers: 1

Kudos [?]: 98 [0], given: 0

### Show Tags

02 Nov 2005, 21:56
I am not able to get any headway n finding t2....

where is our frens lexieqv,qsr,himalaya,gmatt73..???
any hint titleist?
SVP
Joined: 24 Sep 2005
Posts: 1890
Followers: 18

Kudos [?]: 280 [0], given: 0

### Show Tags

02 Nov 2005, 21:58
Titleist wrote:
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.
Director
Joined: 14 Oct 2003
Posts: 587
Location: On Vacation at My Crawford, Texas Ranch
Followers: 1

Kudos [?]: 44 [0], given: 0

### Show Tags

02 Nov 2005, 21:59
duttsit wrote:
I am not able to get any headway n finding t2....

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

http://www.nytimes.com/2005/11/21/international/asia/21prexy.html

SVP
Joined: 24 Sep 2005
Posts: 1890
Followers: 18

Kudos [?]: 280 [0], given: 0

### Show Tags

02 Nov 2005, 22:01
hey, are you sure n > 2 ... I think it should be n > =2
Director
Joined: 14 Oct 2003
Posts: 587
Location: On Vacation at My Crawford, Texas Ranch
Followers: 1

Kudos [?]: 44 [0], given: 0

### Show Tags

02 Nov 2005, 22:02
laxieqv wrote:
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

http://www.nytimes.com/2005/11/21/international/asia/21prexy.html

SVP
Joined: 24 Sep 2005
Posts: 1890
Followers: 18

Kudos [?]: 280 [0], given: 0

### Show Tags

02 Nov 2005, 22:03
VP
Joined: 22 Aug 2005
Posts: 1120
Location: CA
Followers: 1

Kudos [?]: 98 [0], given: 0

### Show Tags

02 Nov 2005, 22:08
Titleist wrote:
laxieqv wrote:
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
Director
Joined: 14 Oct 2003
Posts: 587
Location: On Vacation at My Crawford, Texas Ranch
Followers: 1

Kudos [?]: 44 [0], given: 0

### Show Tags

02 Nov 2005, 22:18
laxieqv wrote:

Very close Laxi, you probably guessed 98.

here is why it's 98 vs. 99

t1 = 1
t2 = -1/2
t3 = -2

t4 = 1
t5 = -1/2
t6 = -2
t10 = 1
..so forth

The sequence repeats itself every 3 terms.

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

http://www.nytimes.com/2005/11/21/international/asia/21prexy.html

Director
Joined: 14 Oct 2003
Posts: 587
Location: On Vacation at My Crawford, Texas Ranch
Followers: 1

Kudos [?]: 44 [0], given: 0

### Show Tags

02 Nov 2005, 22:19
duttsit wrote:
Titleist wrote:
laxieqv wrote:
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

http://www.nytimes.com/2005/11/21/international/asia/21prexy.html

SVP
Joined: 24 Sep 2005
Posts: 1890
Followers: 18

Kudos [?]: 280 [0], given: 0

### Show Tags

02 Nov 2005, 22:41
Titleist wrote:
laxieqv wrote:

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!
Director
Joined: 14 Oct 2003
Posts: 587
Location: On Vacation at My Crawford, Texas Ranch
Followers: 1

Kudos [?]: 44 [0], given: 0

### Show Tags

02 Nov 2005, 22:58
laxieqv wrote:
Titleist wrote:
laxieqv wrote:

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

http://www.nytimes.com/2005/11/21/international/asia/21prexy.html

SVP
Joined: 24 Sep 2005
Posts: 1890
Followers: 18

Kudos [?]: 280 [0], given: 0

### Show Tags

02 Nov 2005, 23:03
Titleist wrote:
laxieqv wrote:
Titleist wrote:
laxieqv wrote:

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
Director
Joined: 14 Oct 2003
Posts: 587
Location: On Vacation at My Crawford, Texas Ranch
Followers: 1

Kudos [?]: 44 [0], given: 0

### Show Tags

02 Nov 2005, 23:04
laxieqv wrote:
Titleist wrote:
laxieqv wrote:
Titleist wrote:
laxieqv wrote:

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

http://www.nytimes.com/2005/11/21/international/asia/21prexy.html

Director
Joined: 14 Oct 2003
Posts: 587
Location: On Vacation at My Crawford, Texas Ranch
Followers: 1

Kudos [?]: 44 [0], given: 0

### Show Tags

02 Nov 2005, 23:08
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

http://www.nytimes.com/2005/11/21/international/asia/21prexy.html

SVP
Joined: 24 Sep 2005
Posts: 1890
Followers: 18

Kudos [?]: 280 [0], given: 0

### Show Tags

02 Nov 2005, 23:09
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
Director
Joined: 14 Oct 2003
Posts: 587
Location: On Vacation at My Crawford, Texas Ranch
Followers: 1

Kudos [?]: 44 [0], given: 0

### Show Tags

02 Nov 2005, 23:11
laxieqv wrote:
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

http://www.nytimes.com/2005/11/21/international/asia/21prexy.html

Display posts from previous: Sort by