GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 19 Feb 2019, 13:11

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.

Close

Request Expert Reply

Confirm Cancel
Events & Promotions in February
PrevNext
SuMoTuWeThFrSa
272829303112
3456789
10111213141516
17181920212223
242526272812
Open Detailed Calendar
  • Free GMAT Prep Hour

     February 20, 2019

     February 20, 2019

     08:00 PM EST

     09:00 PM EST

    Strategies and techniques for approaching featured GMAT topics. Wednesday, February 20th at 8 PM EST
  • Online GMAT boot camp for FREE

     February 21, 2019

     February 21, 2019

     10:00 PM PST

     11:00 PM PST

    Kick off your 2019 GMAT prep with a free 7-day boot camp that includes free online lessons, webinars, and a full GMAT course access. Limited for the first 99 registrants! Feb. 21st until the 27th.

In the infinite sequence a1, a2, ..., an, an equals the sum of all pre

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 52971
In the infinite sequence a1, a2, ..., an, an equals the sum of all pre  [#permalink]

Show Tags

New post 23 Nov 2016, 05:33
14
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

58% (02:48) correct 42% (02:39) wrong based on 98 sessions

HideShow timer Statistics

In the infinite sequence \(a_1\), \(a_2\), ..., \(a_n\), \(a_n\) equals the sum of all previous values in the sequence for all values n>2. If \(a_1=1\) and \(a_3=3\), what is the value of \(\frac{a_{100}}{a_{97}}\)?

A. 3
B. 8
C. 12
D. 27
E. 48

_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Most Helpful Community Reply
SC Moderator
User avatar
D
Joined: 13 Apr 2015
Posts: 1687
Location: India
Concentration: Strategy, General Management
GMAT 1: 200 Q1 V1
GPA: 4
WE: Analyst (Retail)
GMAT ToolKit User Premium Member
Re: In the infinite sequence a1, a2, ..., an, an equals the sum of all pre  [#permalink]

Show Tags

New post 24 Nov 2016, 02:01
6
3
Given: \(a_{1} = 1; a_{3} = 3; a_{2} = a_{3} - a_{1} = 2\)

Sequence: 1, 2, 3, 6, 12, 24 ........ --> Notice that for n > 3, each term is double the previous term
i.e. \(a_{6} = 2a_{5} = 4a_{4}\)

Similarly, \(a_{100} = 2a_{99} = 4a_{98} = 8a_{97}\)

\(a_{100}/a_{97} = 8{a_{97}/a_{97}} = 8\)

Answer: B
General Discussion
Intern
Intern
avatar
B
Joined: 17 Aug 2015
Posts: 11
GPA: 3.87
WE: Research (Telecommunications)
GMAT ToolKit User
Re: In the infinite sequence a1, a2, ..., an, an equals the sum of all pre  [#permalink]

Show Tags

New post 25 Nov 2016, 16:46
1
Using the GP, the CR is 2

General Sum formula for GP =b1*r^n-1/r-1

First term b1 =1; r =2


a100/a97 =2^99/2^96 =2^3 =8 =B
Intern
Intern
avatar
B
Joined: 23 Aug 2015
Posts: 24
Location: India
Concentration: General Management, Human Resources
GMAT 1: 610 Q46 V29
GPA: 3
WE: Consulting (Human Resources)
In the infinite sequence a1, a2, ..., an, an equals the sum of all pre  [#permalink]

Show Tags

New post 23 Jun 2017, 04:06
KalyanVaddagiri wrote:
Using the GP, the CR is 2

General Sum formula for GP =b1*r^n-1/r-1

First term b1 =1; r =2


a100/a97 =2^99/2^96 =2^3 =8 =B



I see that the GP sum formula is [a * ( 1 - r^n) ] / 1 - r. Can you please elaborate on how you got the mentioned formula?
Intern
Intern
avatar
B
Joined: 06 Oct 2017
Posts: 10
GMAT ToolKit User
Re: In the infinite sequence a1, a2, ..., an, an equals the sum of all pre  [#permalink]

Show Tags

New post 24 Dec 2017, 02:03
Bang2919 wrote:
KalyanVaddagiri wrote:
Using the GP, the CR is 2

General Sum formula for GP =b1*r^n-1/r-1

First term b1 =1; r =2


a100/a97 =2^99/2^96 =2^3 =8 =B



I see that the GP sum formula is [a * ( 1 - r^n) ] / 1 - r. Can you please elaborate on how you got the mentioned formula?

Hi,

The formula which you're talking about is used when R<1
Here, we have R>1 which is 2 so that formula is used

Sent from my vivo 1609 using GMAT Club Forum mobile app
Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 9851
Premium Member
Re: In the infinite sequence a1, a2, ..., an, an equals the sum of all pre  [#permalink]

Show Tags

New post 17 Feb 2019, 08:06
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

GMAT Club Bot
Re: In the infinite sequence a1, a2, ..., an, an equals the sum of all pre   [#permalink] 17 Feb 2019, 08:06
Display posts from previous: Sort by

In the infinite sequence a1, a2, ..., an, an equals the sum of all pre

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


cron
Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.