Last visit was: 24 Apr 2024, 00:19 It is currently 24 Apr 2024, 00:19

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
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

# Math : Sequences & Progressions

SORT BY:
Tags:
Show Tags
Hide Tags
Retired Moderator
Joined: 02 Sep 2010
Posts: 615
Own Kudos [?]: 2929 [162]
Given Kudos: 25
Location: London
Q51  V41
SVP
Joined: 12 Oct 2009
Status:<strong>Nothing comes easy: neither do I want.</strong>
Posts: 2279
Own Kudos [?]: 3593 [5]
Given Kudos: 235
Location: Malaysia
Concentration: Technology, Entrepreneurship
Schools: ISB '15 (M)
GMAT 1: 670 Q49 V31
GMAT 2: 710 Q50 V35
General Discussion
Intern
Joined: 26 Sep 2010
Posts: 10
Own Kudos [?]: [0]
Given Kudos: 0
Location: Singapore
WE 1: 6.5 years in Decision Sciences
Retired Moderator
Joined: 02 Sep 2010
Posts: 615
Own Kudos [?]: 2929 [2]
Given Kudos: 25
Location: London
Q51  V41
Re: Math : Sequences & Progressions [#permalink]
2
Kudos
gurpreetsingh wrote:
Great initiative.

Suggestions :

1. Include AM, GM , HM included between 2 numbers.
2. use a_{n} with math tag to get $$a_{n}$$
3. Include more examples.

This post,along with the algebra, is a good initiative to fill the important topics of Math Book that were not included earlier.

Check
Check
Check

Let me know what else ?
Senior Manager
Joined: 24 Jun 2010
Status:Time to step up the tempo
Posts: 273
Own Kudos [?]: 673 [0]
Given Kudos: 50
Location: Milky way
Schools:ISB, Tepper - CMU, Chicago Booth, LSB
Re: Math : Sequences & Progressions [#permalink]
Great initiative. +1 to you.
Manager
Joined: 17 Aug 2009
Posts: 184
Own Kudos [?]: 22 [0]
Given Kudos: 18
Re: Math : Sequences & Progressions [#permalink]
Great one
Kudos to you !
Retired Moderator
Joined: 02 Sep 2010
Posts: 615
Own Kudos [?]: 2929 [3]
Given Kudos: 25
Location: London
Q51  V41
Re: Math : Sequences & Progressions [#permalink]
2
Kudos
1
Bookmarks
added a couple more solved GMAT style questions to the end
Senior Manager
Joined: 31 Mar 2010
Posts: 381
Own Kudos [?]: 66 [0]
Given Kudos: 26
Location: Europe
Re: Math : Sequences & Progressions [#permalink]
Good to know. It can definitely same valuable time.
Manager
Joined: 20 Apr 2010
Posts: 154
Own Kudos [?]: 248 [1]
Given Kudos: 28
Concentration: Finacee, General Management
Schools:ISB, HEC, Said
Q48  V28
Re: Math : Sequences & Progressions [#permalink]
1
Kudos
This is great post but I was just wondering whether we need to know these concepts for GMAT
Retired Moderator
Joined: 02 Sep 2010
Posts: 615
Own Kudos [?]: 2929 [0]
Given Kudos: 25
Location: London
Q51  V41
Re: Math : Sequences & Progressions [#permalink]
There are several questions in the OG that use these concepts. So I think its good to know all this. Plus if you search through the forums you'll find several Qs on sequences and progressions as well
Manager
Joined: 20 Jan 2010
Status:Not afraid of failures, disappointments, and falls.
Posts: 217
Own Kudos [?]: 447 [0]
Given Kudos: 260
Concentration: Technology, Entrepreneurship
WE:Operations (Telecommunications)
Re: Math : Sequences & Progressions [#permalink]
Valuable resource.
Kudos +1
Intern
Joined: 14 Oct 2010
Posts: 1
Own Kudos [?]: 3 [3]
Given Kudos: 1
Re: Math : Sequences & Progressions [#permalink]
3
Kudos
I had a question. I am not sure if this works: "In case of n numbers : AM * HM = GM^n".

This seems to work for 2 numbers but for more than 2, it seems to break, please let me know if I am missing something.
Retired Moderator
Joined: 02 Sep 2010
Posts: 615
Own Kudos [?]: 2929 [0]
Given Kudos: 25
Location: London
Q51  V41
Re: Math : Sequences & Progressions [#permalink]
nitantsharma wrote:
I had a question. I am not sure if this works: "In case of n numbers : AM * HM = GM^n".

This seems to work for 2 numbers but for more than 2, it seems to break, please let me know if I am missing something.

You are correct, this should only hold for special case n=2. Thanks for pointing out
Director
Joined: 09 Jun 2010
Posts: 530
Own Kudos [?]: 523 [0]
Given Kudos: 916
Re: Math : Sequences & Progressions [#permalink]
How can we get the formular for sumation of GEOMETRIC PROGRESSION. Please, prove, so that I do not have to remember the formular but to know the way to get the formular and so can solve the relative questions.
Retired Moderator
Joined: 02 Sep 2010
Posts: 615
Own Kudos [?]: 2929 [0]
Given Kudos: 25
Location: London
Q51  V41
Re: Math : Sequences & Progressions [#permalink]
 ! This proof is beyond the scope of the GMAT

The proof below is based on mathematical induction

To prove : The sum of an n term GP : $$b,br,br^2,...,br^{n-1}$$ is $$b*\frac{r^n-1}{r-1}$$

P(1 term) : The sum of the GP {b} is $$b*\frac{r^1-1}{r-1}=b$$. Which is true trivially

P(n terms) : Let the sum of an n term GP : $$b,br,...,br^{n-1}$$ be $$b*\frac{r^n-1}{r-1}$$

P(n+1 terms) : Consider the n+1 term GP : $$b,br,....,br^n$$
Sum of this GP = Sum of n term GP + $$br^n$$ = $$b*\frac{r^n-1}{r-1} + br^n$$
Sum = $$\frac{b}{r-1} * (r^n - 1 + r^n(r-1))$$
=$$\frac{b}{r-1} *(r^{n+1}-1)$$

Hence P(1) is true
And if we assume P(n) true P(n+1) is true
By mathematical induction P(k) must be true for all k>=1
Hence, proved
Senior Manager
Joined: 23 Apr 2010
Posts: 476
Own Kudos [?]: 352 [0]
Given Kudos: 7
Re: Math : Sequences & Progressions [#permalink]

I think the formula for calculating the sum of n consecutive numbers should be:

$$(lastterm - firstterm)*(lastterm - firstterm + 1)/2$$
Manager
Joined: 15 Nov 2006
Affiliations: SPG
Posts: 232
Own Kudos [?]: 3135 [0]
Given Kudos: 34
Re: Math : Sequences & Progressions [#permalink]
nonameee wrote:

I think the formula for calculating the sum of n consecutive numbers should be:

$$(lastterm - firstterm)*(lastterm - firstterm + 1)/2$$

1,2,3,4,5

let's apply your formula on the above series.

$$\frac{(5-1)*(5-1+1)}{2} = \frac{4*5}{2} = 10$$

this is not correct. let's try another formula.

$$\frac{n}{2}(firstterm + lastterm)$$

$$\frac{5}{2}(5+1) = 15$$

$$\frac{1}{2}(firstterm + lastterm)$$ basically gives you the avg of the series. when you multiply the avg with number of terms (n), you get the sum.

HTH
Senior Manager
Joined: 23 Apr 2010
Posts: 476
Own Kudos [?]: 352 [0]
Given Kudos: 7
Re: Math : Sequences & Progressions [#permalink]
dimitri92, thanks. I must have made a computational error.
Manager
Joined: 08 Nov 2010
Posts: 204
Own Kudos [?]: 496 [0]
Given Kudos: 161
Q50  V41
GPA: 3.9
Re: Math : Sequences & Progressions [#permalink]
i know i read it somewhere, but i cant find it now. What are the ways to get the full Math book?
Intern
Joined: 29 May 2011
Posts: 5
Own Kudos [?]: 6 [0]
Given Kudos: 0
Schools:HBS
GPA: 3.8
Re: Math : Sequences & Progressions [#permalink]
 The general sum of a n term GP with common ratio r is given by

For sum of a GP:
When r > 1, the denominator is (r-1)
When r < 1, the denominator is (1-r)
Re: Math : Sequences & Progressions [#permalink]
1   2   3   4
Moderator:
Math Expert
92883 posts