NEW HERE? LEARN MORE
closeclose
Last visit was: 25 Apr 2024, 08:45 It is currently 25 Apr 2024, 08:45
Decision Tracker
My Rewards
New posts
New comers' posts

Close
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
Your Progress

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
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

exponents-Gprep

User avatar
tejal777
Senior Manager
Senior Manager
Joined: 25 Oct 2008
Posts: 361
Own Kudos [?]: 6508 [0]
Given Kudos: 100
Location: Kolkata,India
 Q44  V38
Send PM
exponents-Gprep [#permalink] New post   03 Nov 2009, 04:47
00:00
A
B
C
D
E

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct 100% (02:10) wrong based on 1 sessions
Hide Show timer Statistics
What is the value of \(2 + 2 + 2^2 + 2^3 + 2^4 + 2^5 + 2^6 + 2^7 + 2^8? \)

Got the correct ans by the long long long approach..Shorter way??



Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Problem Solving (PS) Forum
Still interested in this question? Check out the "Best Topics" block below for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
User avatar
asterixmatrix
Manager
Manager
Joined: 12 Oct 2009
Posts: 65
Own Kudos [?]: 146 [0]
Given Kudos: 3
Send PM
Re: exponents-Gprep [#permalink] New post   03 Nov 2009, 06:06
tejal777 wrote:
What is the value of \(2 + 2 + 2^2 + 2^3 + 2^4 + 2^5 + 2^6 + 2^7 + 2^8? \)

Got the correct ans by the long long long approach..Shorter way??


we can consider this as 2 + GP series (2+ 2^2----+ 2^8)
then sum of n terms in GP series for this will be 2(2^8 -1)/(2-1) = 510

so we get 510 +2 = 512
User avatar
lagomez
VP
VP
Joined: 05 Mar 2008
Posts: 1226
Own Kudos [?]: 518 [1]
Given Kudos: 31
Send PM
Re: exponents-Gprep [#permalink] New post   03 Nov 2009, 08:21
1
Kudos
tejal777 wrote:
What is the value of \(2 + 2 + 2^2 + 2^3 + 2^4 + 2^5 + 2^6 + 2^7 + 2^8? \)

Got the correct ans by the long long long approach..Shorter way??


This is more about recognizing a pattern:

2 + 2 = 2^2

2^2 + 2^2 = 2^2(1 + 1) because we factor out the 2^2
2^2(2) = 2^3

2^3 + 2^3 = 2^3 (1+1) = 2^4

you can pretty much stop after that and recognize that you will eventually get 2^8 + 2^8 = 2^9

There usually tends to a be a pattern in these type of questions.
User avatar
study
Manager
Manager
Joined: 05 Oct 2008
Posts: 160
Own Kudos [?]: 3546 [0]
Given Kudos: 22
Send PM
Re: exponents-Gprep [#permalink] New post   15 Nov 2009, 10:11
What is GP and what is the formula about?

Bunuel, can you please explain this one.

Thank you.
User avatar
h2polo
Manager
Manager
Joined: 13 Aug 2009
Posts: 102
Own Kudos [?]: 345 [1]
Given Kudos: 16
Schools: Sloan '14 (S)
Send PM
Re: exponents-Gprep [#permalink] New post   15 Nov 2009, 11:21
1
Kudos
GP is short for Geometric Progression. You can check out the wikipedia article for a detailed explaination:

https://en.wikipedia.org/wiki/Geometric_progression

But don't get caught up on trying to remember formulas. The key is to understand what you are looking at.

Just like lagomez said, it is about pattern recognition:

Here is the pattern I used:

2+2+2^2+2^3+2^4+2^5+2^6+2^7+2^8
Factor out the two:
2*(1+1+2+2^2+2^3+2^4+2^5+2^6+2^7)=2*(2+2^1+2^2+2^3+2^4+2^5+2^6+2^7)
Keep factoring out the two...
2*2*(2+2+2^2+2^3+2^4+2^5+2^6)
2*2*2*(2+2+2^2+2^3+2^4+2^5)
2*2*2*2*(2+2+2^2+2^3+2^4)
2*2*2*2*2*(2+2+2^2+2^3)
2*2*2*2*2*2*(2+2+2^2)
2*2*2*2*2*2*2*(2+2)
2*2*2*2*2*2*2*2*(2)
OR
2^9=512
User avatar
ctrlaltdel
Manager
Manager
Joined: 24 Jul 2009
Posts: 61
Own Kudos [?]: 461 [2]
Given Kudos: 124
Location: United States
GMAT 1: 590 Q48 V24
Send PM
Re: exponents-Gprep [#permalink] New post   15 Nov 2009, 11:24
2
Kudos
study,

Here u go....hope it is useful.

Cheers

Kudos, if u feel it was helpful.
Attachments

arith_and_geom_progressions.pdf [182.25 KiB]
Downloaded 481 times

User avatar
ctrlaltdel
Manager
Manager
Joined: 24 Jul 2009
Posts: 61
Own Kudos [?]: 461 [2]
Given Kudos: 124
Location: United States
GMAT 1: 590 Q48 V24
Send PM
Re: exponents-Gprep [#permalink] New post   15 Nov 2009, 12:40
2
Kudos
One more...Source:tcy

Kudos if u find it helpful.
Attachments

sequence.pdf [99.51 KiB]
Downloaded 190 times

User avatar
study
Manager
Manager
Joined: 05 Oct 2008
Posts: 160
Own Kudos [?]: 3546 [0]
Given Kudos: 22
Send PM
Re: exponents-Gprep [#permalink] New post   19 Jun 2010, 03:25
I tried to apply the GP formula but something is wrong - Can someone help please. Thanks.


a = the first term
r = the common ratio,
Tn = nth term and
Sn = sum of n terms

Sum of first n terms of G.P:
Sn = [a (r^n - 1)] / a(r - 1)
where r > 1


Sum
[a (r^n - 1)] = 2 (2^10 - 1) = 2 * (1024 -1) = 2*1023
a(r - 1) = 2 ( 2 - 1) = 2

Hence sum = 2 * 1023 / 2 = 1023 that is incorrect
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92914
Own Kudos [?]: 618955 [0]
Given Kudos: 81595
Send PM
CAT Tests Forum Quiz Mode
Re: exponents-Gprep [#permalink] New post   19 Jun 2010, 04:06
Expert Reply
study wrote:
I tried to apply the GP formula but something is wrong - Can someone help please. Thanks.


a = the first term
r = the common ratio,
Tn = nth term and
Sn = sum of n terms

Sum of first n terms of G.P:
Sn = [a (r^n - 1)] / a(r - 1)
where r > 1


Sum
[a (r^n - 1)] = 2 (2^10 - 1) = 2 * (1024 -1) = 2*1023
a(r - 1) = 2 ( 2 - 1) = 2

Hence sum = 2 * 1023 / 2 = 1023 that is incorrect


Sum of the terms of geometric progression is given by: \(Sum=\frac{a*(r^{n}-1)}{r-1}\), where \(a\) is the first term, \(n\) # of terms and \(r\) is a common ratio \(>1\).

In our original question we have 2 plus G.P. with 8 terms, so:

\(2+(2+2^2+2^3+2^4+2^5+2^6+2^7+2^8)=2+\frac{2*(2^{8}-1)}{2-1}=1024\)



Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Problem Solving (PS) Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
GMAT Club Bot
gmatclubot
Re: exponents-Gprep [#permalink]
19 Jun 2010, 04:06
Moderators:
Bunuel
Math Expert
92914 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions