BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

GMAT PREP QUES?

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Master | Next Rank: 500 Posts
Posts: 446
Joined: Thu Jul 26, 2007 1:07 pm
Thanked: 6 times

GMAT PREP QUES?

by dferm » Tue Feb 26, 2008 10:52 am
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 sume of the first 10 terms in the sequence, then T is:



A. greater than 2
B. between 1 and 2
C. between ½ and 1
D. between ¼ and ½
E. less than ¼


Please explain.
Top
Source: — Problem Solving |
Master | Next Rank: 500 Posts
Posts: 188
Joined: Sun Dec 23, 2007 7:40 am
Location: INDIA
Thanked: 4 times

by senthil » Tue Feb 26, 2008 11:07 am
I am not able to decipher the expression u have said ..
is it
(-1)^k + (1/2)^k

or

(-1)^k + (3/2)^k


Thanks
Senthil
Top
Master | Next Rank: 500 Posts
Posts: 188
Joined: Sun Dec 23, 2007 7:40 am
Location: INDIA
Thanked: 4 times

by senthil » Tue Feb 26, 2008 11:36 am
I am not able to decipher the expression u have said ..
is it
(-1)^k + (1/2)^k

or

(-1)^k + (3/2)^k


Thanks
Senthil
Top
Master | Next Rank: 500 Posts
Posts: 446
Joined: Thu Jul 26, 2007 1:07 pm
Thanked: 6 times

GMAT PREP

by dferm » Tue Feb 26, 2008 2:18 pm
Its to the power of k+1
Top
Senior | Next Rank: 100 Posts
Posts: 36
Joined: Mon Jan 28, 2008 4:12 pm
Location: Montreal, Canada
Thanked: 2 times

Re: GMAT PREP QUES?

by Kaunteya » Tue Feb 26, 2008 2:33 pm
dferm 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 sume of the first 10 terms in the sequence, then T is:



A. greater than 2
B. between 1 and 2
C. between ½ and 1
D. between ¼ and ½
E. less than ¼


Please explain.
Hey guy, check the bolded item above! You said it was ^k+1 so is the equation ((-1)^k+1))(1/(2^k) or ((-1)^k+1)((1/2)^k). It is difficult to HELP YOU if you can't simply post the question correctly.
Top
Master | Next Rank: 500 Posts
Posts: 188
Joined: Sun Dec 23, 2007 7:40 am
Location: INDIA
Thanked: 4 times

by senthil » Wed Feb 27, 2008 2:33 am
The sum will be between 1/2 to 1.

This is a geometric progression series.Thereby I feel even if u sum to 20+ numbers it wud not be more than 1.
There for the answer shud be C.

Let me know if I am wrong!

Senthil :D
Top
User avatar
Legendary Member
Posts: 543
Joined: Fri Jan 18, 2008 1:01 am
Thanked: 43 times
GMAT Score:580

by codesnooker » Wed Feb 27, 2008 3:40 am
The answer is D.

Let me know if I am incorrect.
Top
Master | Next Rank: 500 Posts
Posts: 132
Joined: Tue Oct 07, 2008 4:59 pm
Thanked: 4 times

Gmatprep Arithm

by vladmire » Thu Dec 11, 2008 6:47 pm
Does anyone know how to solve this question
Attachments
equal.jpg
Top
Senior | Next Rank: 100 Posts
Posts: 47
Joined: Wed Oct 08, 2008 11:29 am
Location: Toronto, Ontario
Thanked: 5 times

by anayeri » Thu Dec 11, 2008 10:35 pm
I think answer's A, here's why:

formula for sum of numbers in a set is: (n/2)*(first number + last number) (ie 2+3+4+5 = (4/2)*(2+5) = 14.)

So, sum of this sequence would be:

(10/2)*[((-1)^(1+1)*(1/(2^1))] + [((-1)^(1+10)*(1/(2^10))]
=5*[(1)*(1/2)] + (-1)*(1/(2^10))
=5*[(1/2)+(-1/1024)]
=5*(512/1024)-(1/1024)
=5*(511/1024)
=5* something slightly smaller than 1/2, which means T=2.5something, which is greater than 2, thus A.

Any comments/thoughts on this approach?
Top
Senior | Next Rank: 100 Posts
Posts: 61
Joined: Mon Nov 17, 2008 11:35 pm
Thanked: 6 times
Followed by:1 members

by brb588 » Thu Dec 11, 2008 10:39 pm
I just plugged in the first few integers and looked for a pattern. When k=1, the corresponding amount is 1/2, when k=2, it is -1/4, k=3 is 1/8, k=4 is -1/16, and so on. You can stop computing for k here because you can see a pattern.

Now add the ks, and look for another pattern:

I have 1/2 of a t-pizza, you take 1/4 of a pizza, leaving me with 1/4 of a pizza. You give me 1/8 of a pizza back. I have now 1/4 + 1/8 = 3/8. You take 1/16 away, and that leaves me with 5/16.

If you go all the way to k=10, you can never go below 1/4 or above 1/2. Therefore, it's D.

Does this makes sense?
Last edited by brb588 on Thu Dec 11, 2008 10:47 pm, edited 2 times in total.
Top
Senior | Next Rank: 100 Posts
Posts: 47
Joined: Wed Oct 08, 2008 11:29 am
Location: Toronto, Ontario
Thanked: 5 times

by anayeri » Thu Dec 11, 2008 10:40 pm
Nevermind, I realized shortly after I wrote my post that my rationale was based on consecutive numbers, and actually has no meaning in this question.

Here's a good explanation by Ron: https://www.manhattangmat.com/forums/for ... t1950.html
Top
Master | Next Rank: 500 Posts
Posts: 132
Joined: Tue Oct 07, 2008 4:59 pm
Thanked: 4 times

Arithmetic

by vladmire » Fri Dec 12, 2008 5:50 pm
Isn't the (-1^1-1)(1/2^1) = -1/2 instead of 1/2
k= 1


brb588 wrote:I just plugged in the first few integers and looked for a pattern. When k=1, the corresponding amount is 1/2, when k=2, it is -1/4, k=3 is 1/8, k=4 is -1/16, and so on. You can stop computing for k here because you can see a pattern.

Now add the ks, and look for another pattern:

I have 1/2 of a t-pizza, you take 1/4 of a pizza, leaving me with 1/4 of a pizza. You give me 1/8 of a pizza back. I have now 1/4 + 1/8 = 3/8. You take 1/16 away, and that leaves me with 5/16.

If you go all the way to k=10, you can never go below 1/4 or above 1/2. Therefore, it's D.

Does this makes sense?
Top
Senior | Next Rank: 100 Posts
Posts: 61
Joined: Mon Nov 17, 2008 11:35 pm
Thanked: 6 times
Followed by:1 members

Re: Arithmetic

by brb588 » Fri Dec 12, 2008 9:13 pm
vladmire wrote:Isn't the (-1^1-1)(1/2^1) = -1/2 instead of 1/2
k= 1
You got the equation wrong, it's (-1)^(1+1) * 1/(2^1) =

-1^2 * 1/2 =

1 * 1/2 =

1/2
Top
User avatar
Legendary Member
Posts: 575
Joined: Tue Nov 04, 2008 2:58 am
Location: India
Thanked: 18 times
Followed by:4 members
GMAT Score:710

by rahulg83 » Sat Dec 13, 2008 11:21 pm
I ll go for D if u consider (-1)^(K+1) * (1/2)^k..
put K from 1 to 10 and just expand the series...
U'll get something like all the odd powers of 1/2 from 1 to 9 minus all the even powers of 1/2 from 2 to 10. We'll get two GP's with C.R. 1/2. Solving them we'll get answer as 1023/2048 which is less than 1/2 nut greater than 1/4
Top
Post new topic Post Reply
• Page 1 of 1