It is currently 17 Nov 2017, 12:56

### 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 every integer k from 1 to 10 inclusive the kth term of a

Author Message
Manager
Joined: 13 Apr 2006
Posts: 56

Kudos [?]: 13 [0], given: 0

For every integer k from 1 to 10 inclusive the kth term of a [#permalink]

### Show Tags

11 Jun 2006, 17:04
00:00

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 2 sessions

### HideShow timer Statistics

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

For every integer k from 1 to 10 inclusive the kth term of a certain sequence is given by -1^(k+1)*(1/2^k). If T is the sum of the first 10 terms, then T is:

a. greater than 2
b. between 1 and 2
c. between 1/2 and 1
d. between 1/4 and 1/2
e. less than 1/4

Please explain your answer. This to me was taking too long so I guessed and moved on. Is there a quick, efficient way to execute this?

Kudos [?]: 13 [0], given: 0

VP
Joined: 29 Dec 2005
Posts: 1337

Kudos [?]: 69 [0], given: 0

Re: GMAT Prep Algebra PS [#permalink]

### Show Tags

11 Jun 2006, 18:07
kuristar wrote:
For every integer k from 1 to 10 inclusive the kth term of a certain sequence is given by -1^(k+1)*(1/2^k). If T is the sum of the first 10 terms, then T is:

a. greater than 2
b. between 1 and 2
c. between 1/2 and 1
d. between 1/4 and 1/2
e. less than 1/4

i guess -1^(k+1)*(1/2^k) = (-1)^(k+1)*(1/2^k)

1st term = (-1)^(1+1)*(1/2^k) = 1/2
2nd term = (-1)^(k+1)*(1/2^k) = -1/4
3rd term = (-1)^(k+1)*(1/2^k) = 1/8
4th term = (-1)^(k+1)*(1/2^k) = -1/16

now we can get every term by multiplying the prededing term by -1/2. so..

5th = 4th term (-1/2) = -1/16 (-1/2) = 1/32
6th = - 1/64
7th = 1/128
8th = -1/256
9th = 1/512
10th = -1/1024

get the sum of every 2 conseqcutive terms
sum of 1st and 2nd term = 1/2 - 1/4 = 1/4
sum of 3rd and 4th term = 1/8 - 1/16 = 1/16

similarly the next term becames = (1/16)(1/4)=1/64

the next term becames = (1/64)(1/4)=1/256

the final term becames = (1/256)(1/4)=1/1024

lets add them all =1/4 +1/16+1/64+1/256+1/1024 = 331/1024

so this value is ====>>>>>

1/4 < 331/1024 < 1/3

it is D.

Kudos [?]: 69 [0], given: 0

SVP
Joined: 30 Mar 2006
Posts: 1728

Kudos [?]: 101 [1], given: 0

### Show Tags

12 Jun 2006, 04:48
1
KUDOS
1st number of the sequence = 1/2
2nd number = -1/4
3rd number = 1/8
Now this is a geometric series with r = -1/2

Sum = a(1-r^n)/1-r
= 1/2(1- (-1/2)^10)/1-(-1/2)

= 2^10 -1/3*2^10
~<1/3
Hence D

Kudos [?]: 101 [1], given: 0

Manager
Joined: 10 May 2006
Posts: 186

Kudos [?]: 5 [0], given: 0

Location: USA

### Show Tags

12 Jun 2006, 14:48
K1= 1/2
K2 = (-1/4)
K3 = 1/8
K4 = (-1/16)

and so forth...as K gets larger, the numbers get smaller and smaller.

Group the numbers together and add together
ie) K1+ K2 = 1/2 + -1/4 = 1/4
K3 +K4 = 1/8 + -1/16 = 1/8

as we continue this pattern, the figures will become smaller and smaller positive numbers.

Therefore we know that the answer is definitely greater than 1/4, but since the numbers get smaller and smaller, the best answer is D, between 1/4 and 1/2.

Kudos [?]: 5 [0], given: 0

12 Jun 2006, 14:48
Display posts from previous: Sort by