Oct 14 08:00 PM PDT  11:00 PM PDT Join a 4day FREE online boot camp to kick off your GMAT preparation and get you into your dream bschool in R2.**Limited for the first 99 registrants. Register today! Oct 15 12:00 PM PDT  01:00 PM PDT Join this live GMAT class with GMAT Ninja to learn to conquer your fears of long, kooky GMAT questions. Oct 16 08:00 PM PDT  09:00 PM PDT EMPOWERgmat is giving away the complete Official GMAT Exam Pack collection worth $100 with the 3 Month Pack ($299) Oct 19 07:00 AM PDT  09:00 AM PDT Does GMAT RC seem like an uphill battle? eGMAT is conducting a free webinar to help you learn reading strategies that can enable you to solve 700+ level RC questions with at least 90% accuracy in less than 10 days. Sat., Oct 19th at 7 am PDT Oct 20 07:00 AM PDT  09:00 AM PDT Get personalized insights on how to achieve your Target Quant Score.
Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 21 Apr 2010
Posts: 7

In the infinite sequence a1, a2, a3, ..., an, each term after the firs
[#permalink]
Show Tags
21 Apr 2010, 06:49
Question Stats:
81% (01:38) correct 19% (02:06) wrong based on 209 sessions
HideShow timer Statistics
In the infinite sequence \(a_1\), \(a_2\), \(a_3\),...., \(a_n\), each term after the first is equal to twice the previous term. If \(a_5a_2=12\), what is the value of a_1? A. 4 B. 24/7 C. 2 D. 12/7 E. 6/7
Official Answer and Stats are available only to registered users. Register/ Login.




Math Expert
Joined: 02 Sep 2009
Posts: 58313

Re: If the infinite sequence a1, a2, a3, ..., an, ..., each term
[#permalink]
Show Tags
18 Jun 2012, 01:30
In the infinite sequence \(a_1\), \(a_2\), \(a_3\),...., \(a_n\), each term after the first is equal to twice the previous term. If \(a_5a_2=12\), what is the value of \(a_1\)? A. 4 B. 24/7 C. 2 D. 12/7 E. 6/7 The formula for calculating \(n_{th}\) term would be \(a_n=2^{n1}*a_1\) . So: \(a_5=2^4*a_1\); \(a_2=2*a_1\); Given: \(a_5a_2=2^4*a_12*a_1=12\) > \(2^4*a_12*a_1=12\) > \(a_1=\frac{12}{14}=\frac{6}{7}\). Answer: E. Hope it's clear.
_________________




Senior Manager
Status: Up again.
Joined: 31 Oct 2010
Posts: 464
Concentration: Strategy, Operations
GMAT 1: 710 Q48 V40 GMAT 2: 740 Q49 V42

Re: In the infinite sequence a1, a2, a3, ..., an, each term after the firs
[#permalink]
Show Tags
17 Feb 2011, 06:49
Baten80 wrote: In the infinite sequence a1, a2, a3,...., an, each term after the first is equal to twice the previous term. If a5a2=12, what is the value of a1?
A. 4 B.24/7 C.2 D.12/7 E.6/7 Let the \(a1= x\) therefore, \(a2=2x, a3=4x, a4=8x, a5=16x.\) It is given that \(a5a2=12\), that means: \(16x2x=12\); \(14x=12\), therefore \(x=\frac{6}{7}= a1.\) Answer is E.
_________________
My GMAT debrief: http://gmatclub.com/forum/from620to710mygmatjourney114437.html



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9697
Location: Pune, India

Re: If the infinite sequence a1, a2, a3, ..., an, ..., each term
[#permalink]
Show Tags
18 Jun 2012, 02:50
Stiv wrote: In the infinite sequence \(a_1\), \(a_2\), \(a_3\),...., \(a_n\), each term after the first is equal to twice the previous term. If \(a_5a_2=12\), what is the value of \(a_1\)?
A. 4 B. 24/7 C. 2 D. 12/7 E. 6/7 First step for sequence questions is writing down the first few terms. \(a_2 = 2*a_1\) \(a_3 = 2*a_2 = 2*2*a_1\) and so on.. \(a_5  a_2 = 2*2*2*2*a_1  2*a_1 = 14 * a_1 = 12\) So, \(a_1 = 12/14 = 6/7\) For more on sequences, check out: http://www.veritasprep.com/blog/2012/03 ... sequences/
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >



Verbal Forum Moderator
Joined: 10 Oct 2012
Posts: 591

Re: In the infinite sequence a1, a2,
[#permalink]
Show Tags
19 Nov 2013, 03:40
amgelcer wrote: In the infinite sequence a1, a2, a3, ..., an, ..., each term after the first is equal to twice the previous term. If a5  a2, = 12, what is the value of a1?
(A) 4
(B) 24/7
(C) 2
(D) 12/7
(E) 6/7
 +KUDOS is the way to say THANKS It is a Geometric Progression, with the common ratio as 2. Thus, as \(t_n = a*r^{n1}\) , where a is the first term and r is the common ratio. \(a_5 = a_1*2^4\)and \(a_2 = a_1*2^1\) Thus,\(a_5a_2 = a_1*14 = 12 \to a_1 = \frac{6}{7}\) E.
_________________



Target Test Prep Representative
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2817

Re: If the infinite sequence a1, a2, a3, ..., an, ..., each term
[#permalink]
Show Tags
02 Sep 2017, 07:08
alimad wrote: In the infinite sequence \(a_1\), \(a_2\), \(a_3\),...., \(a_n\), each term after the first is equal to twice the previous term. If \(a_5a_2=12\), what is the value of \(a_1\)?
A. 4 B. 24/7 C. 2 D. 12/7 E. 6/7 We can let a_1 = x, a_2 = 2x, a_3 = 4x, a_4 = 8x and a_5 = 16x. Thus: 16x  2x = 12 14x = 12 x = 12/14 = 6/7 Answer: E
_________________
5star rated online GMAT quant self study course See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews
If you find one of my posts helpful, please take a moment to click on the "Kudos" button.



Intern
Joined: 04 Sep 2017
Posts: 18

Re: In the infinite sequence a1, a2, a3, ..., an, each term after the firs
[#permalink]
Show Tags
24 Feb 2018, 16:30
Bunuel wrote: In the infinite sequence \(a_1\), \(a_2\), \(a_3\),...., \(a_n\), each term after the first is equal to twice the previous term. If \(a_5a_2=12\), what is the value of a_1?
A. 4 B. 24/7 C. 2 D. 12/7 E. 6/7
The formula for calculating \(n_{th}\) term would be \(a_n=2^{n1}*a_1\) . So: \(a_5=2^4*a_1\); \(a_2=2*a_1\);
Given: \(a_5a_2=2^4*a_12*a_1=12\) > \(2^4*a_12*a_1=12\) > \(a_1=\frac{12}{14}=\frac{6}{7}\).
Answer: E.
Hope it's clear. Can someone help me out here? I dont know if I am reading the question correctly but it says each term after the first term is equal to twice the previous term but the solution above shows it as two times the previous term times the first term. I am not seeing how that makes sense? Shouldnt it be \(a_5=2^4?\)



Senior SC Moderator
Joined: 22 May 2016
Posts: 3536

In the infinite sequence a1, a2, a3, ..., an, each term after the firs
[#permalink]
Show Tags
24 Feb 2018, 21:47
teamryan15 wrote: Bunuel wrote: In the infinite sequence \(a_1\), \(a_2\), \(a_3\),...., \(a_n\), each term after the first is equal to twice the previous term. If \(a_5a_2=12\), what is the value of a_1?
A. 4 B. 24/7 C. 2 D. 12/7 E. 6/7
The formula for calculating \(n_{th}\) term would be \(a_n=2^{n1}*a_1\) . So: \(a_5=2^4*a_1\); \(a_2=2*a_1\);
Given: \(a_5a_2=2^4*a_12*a_1=12\) > \(2^4*a_12*a_1=12\) > \(a_1=\frac{12}{14}=\frac{6}{7}\).
Answer: E.
Hope it's clear. Can someone help me out here? I dont know if I am reading the question correctly but it says each term after the first term is equal to twice the previous term but the solution above shows it as two times the previous term times the first term. I am not seeing how that makes sense? Shouldnt it be \(a_5=2^4?\) teamryan15 I think I see where you're a little off. The first term is not 1. You are focused on just the coefficient / multiplier, I think. If \(A_1\) were 1, then yes, \(A_5\) would = \(2^4\). We would have: \(A_1 = 1\) \(A_2 = 2\) \(A_3 = 4\) \(A_4 = 8\) \(A_5 = 16 = 2^4\) The first term is \(a\), not 1. Thus: \(A_1 = a_1\) \(A_2 = (2*a_1) = 2a_1 = 2^1*a_1\) \(A_3 = (2*2a_1)= 4a_1 = 2^2*a_1\) \(A_4 = (2*4a_1)= 8a_1 = 2^3* a_1\) \(A_5 = (2*8a_1) = 16a_1 = 2^4*a_1\) Hope that helps.
_________________
SC Butler has resumed! Get two SC questions to practice, whose links you can find by date, here.Choose life.



NonHuman User
Joined: 09 Sep 2013
Posts: 13088

Re: If the infinite sequence a1, a2, a3, ..., an, ..., each term
[#permalink]
Show Tags
02 Sep 2018, 15:34
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.
_________________




Re: If the infinite sequence a1, a2, a3, ..., an, ..., each term
[#permalink]
02 Sep 2018, 15:34






