Last visit was: 23 Apr 2026, 16:13 It is currently 23 Apr 2026, 16:13
Home
Messages
Tests
Schools
Events
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
Back to Forum
Create Topic
505-555 (Easy)|   Sequences|         
User avatar
ITC
User avatar
Joined: 21 Apr 2010
Last visit: 26 Apr 2010
Posts: 6
Own Kudos:
42
 [40]
Given Kudos: 6
Posts: 6
Kudos: 42
 [40]
In the infinite sequence a1, a2, a3, ..., an, each term after the firs 21 Apr 2010, 06:49
5
Kudos
Add Kudos
34
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

15% (low)

Question Stats:

85% (01:38) correct 15% (02:13) wrong based on 1478 sessions

History

Date
Time
Result
Not Attempted Yet
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 \(a_5-a_2=12\), what is the value of a_1?

A. 4
B. 24/7
C. 2
D. 12/7
E. 6/7
ShowHide Answer
Official Answer
E
Solving this question helps. Taking a timed set of similar questions in GMAT Club Forum Quiz → is even better.
Most Helpful Reply
User avatar
gmatpapa
User avatar
Joined: 31 Oct 2010
Last visit: 25 Aug 2018
Posts: 415
Own Kudos:
2,642
 [15]
Given Kudos: 75
Status:Up again.
Concentration: Strategy, Operations
Schools: Ivey '16 (A) Carlson '17 (A) McCombs '17 (A) W.P. Carey '17 (M$)
GMAT 1: 740 Q49 V42
GMAT 2: 710 Q48 V40
Schools: Ivey '16 (A) Carlson '17 (A) McCombs '17 (A) W.P. Carey '17 (M$)
GMAT 2: 710 Q48 V40
Posts: 415
Kudos: 2,642
 [15]
In the infinite sequence a1, a2, a3, ..., an, each term after the firs 17 Feb 2011, 06:49
10
Kudos
Add Kudos
5
Bookmarks
Bookmark this Post
Baten80
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
Show more

Let the \(a1= x\)
therefore, \(a2=2x, a3=4x, a4=8x, a5=16x.\)

It is given that \(a5-a2=12\), that means: \(16x-2x=12\); \(14x=12\), therefore \(x=\frac{6}{7}= a1.\)

Answer is E.
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 23 Apr 2026
Posts: 109,785
Own Kudos:
810,869
 [8]
Given Kudos: 105,853
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 109,785
Kudos: 810,869
 [8]
In the infinite sequence a1, a2, a3, ..., an, each term after the firs Updated on: 07 Oct 2025, 14:09
Originally posted by Bunuel on 18 Jun 2012, 01:30.
Last edited by Bunuel on 07 Oct 2025, 14:09, edited 1 time in total.
Kudos
Add Kudos
8
Bookmarks
Bookmark this Post
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 \(a_5-a_2=12\), 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 \(a_n=2^{n-1}*a_1\) . So:

\(a_5=2^4*a_1\);
\(a_2=2*a_1\);

Given:

\(a_5-a_2=2^4*a_1-2*a_1=12\)

\(2^4*a_1-2*a_1=12\)

\(a_1=\frac{12}{14}=\frac{6}{7}\).

Answer: E.

Hope it's clear.
General Discussion
User avatar
KarishmaB
User avatar
Joined: 16 Oct 2010
Last visit: 23 Apr 2026
Posts: 16,441
Own Kudos:
79,396
 [5]
Given Kudos: 484
Location: Pune, India
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 16,441
Kudos: 79,396
 [5]
In the infinite sequence a1, a2, a3, ..., an, each term after the firs Updated on: 08 Oct 2022, 22:05
Originally posted by KarishmaB on 18 Jun 2012, 02:50.
Last edited by KarishmaB on 08 Oct 2022, 22:05, edited 1 time in total.
3
Kudos
Add Kudos
2
Bookmarks
Bookmark this Post
Stiv
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 \(a_5-a_2=12\), what is the value of \(a_1\)?

A. 4
B. 24/7
C. 2
D. 12/7
E. 6/7
Show more

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, \(a_1 = 12/14 = 6/7\)
User avatar
mau5
User avatar
Verbal Forum Moderator
Joined: 10 Oct 2012
Last visit: 31 Dec 2024
Posts: 478
Own Kudos:
3,386
 [1]
Given Kudos: 141
Posts: 478
Kudos: 3,386
 [1]
In the infinite sequence a1, a2, a3, ..., an, each term after the firs 19 Nov 2013, 03:40
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
amgelcer
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
Show more

It is a Geometric Progression, with the common ratio as 2.

Thus, as \(t_n = a*r^{n-1}\) , 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,\(a_5-a_2 = a_1*14 = 12 \to a_1 = \frac{6}{7}\)

E.
User avatar
JeffTargetTestPrep
User avatar
Target Test Prep Representative
Joined: 04 Mar 2011
Last visit: 05 Jan 2024
Posts: 2,974
Own Kudos:
8,710
Given Kudos: 1,646
Status:Head GMAT Instructor
Affiliations: Target Test Prep
Expert
Expert reply
Posts: 2,974
Kudos: 8,710
In the infinite sequence a1, a2, a3, ..., an, each term after the firs 02 Sep 2017, 07:08
Kudos
Add Kudos
Bookmarks
Bookmark this Post
alimad
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 \(a_5-a_2=12\), what is the value of \(a_1\)?

A. 4
B. 24/7
C. 2
D. 12/7
E. 6/7
Show more

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
avatar
teamryan15
avatar
Joined: 04 Sep 2017
Last visit: 17 Dec 2018
Posts: 14
Own Kudos:
11
Given Kudos: 5
Posts: 14
Kudos: 11
In the infinite sequence a1, a2, a3, ..., an, each term after the firs 24 Feb 2018, 16:30
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
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 \(a_5-a_2=12\), 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 \(a_n=2^{n-1}*a_1\) . So:
\(a_5=2^4*a_1\);
\(a_2=2*a_1\);

Given: \(a_5-a_2=2^4*a_1-2*a_1=12\) --> \(2^4*a_1-2*a_1=12\) --> \(a_1=\frac{12}{14}=\frac{6}{7}\).

Answer: E.

Hope it's clear.
Show more

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 \(a_5=2^4?\)
User avatar
generis
User avatar
Senior SC Moderator
Joined: 22 May 2016
Last visit: 18 Jun 2022
Posts: 5,258
Own Kudos:
37,727
Given Kudos: 9,464
Expert
Expert reply
Posts: 5,258
Kudos: 37,727
In the infinite sequence a1, a2, a3, ..., an, each term after the firs 24 Feb 2018, 21:47
Kudos
Add Kudos
Bookmarks
Bookmark this Post
teamryan15
Bunuel
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 \(a_5-a_2=12\), 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 \(a_n=2^{n-1}*a_1\) . So:
\(a_5=2^4*a_1\);
\(a_2=2*a_1\);

Given: \(a_5-a_2=2^4*a_1-2*a_1=12\) --> \(2^4*a_1-2*a_1=12\) --> \(a_1=\frac{12}{14}=\frac{6}{7}\).

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 \(a_5=2^4?\)
Show more
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.
User avatar
yannichc
User avatar
Joined: 28 Aug 2022
Last visit: 19 Jan 2024
Posts: 30
Own Kudos:
3
Given Kudos: 85
Posts: 30
Kudos: 3
In the infinite sequence a1, a2, a3, ..., an, each term after the firs 06 Mar 2023, 23:09
Kudos
Add Kudos
Bookmarks
Bookmark this Post
if someone gets confused they can do it this way by eliminating answers

2, 4 and 24/7 (which is ~3) are all too big for a1 because for e.g. if a1=2 then a5 would be 32 but a2 would 4 and 32-4=28 and not 12

can either guess between 12/7 and 6/7 and quickly calculate that 12/7 =a1 and a5 would be 192/7 and 192/7-24/7 would not give you 12.

Choose answer E
User avatar
Ranjansudhanshu
User avatar
Joined: 30 Jul 2025
Last visit: 21 Feb 2026
Posts: 2
Given Kudos: 27
Posts: 2
Kudos: 0
In the infinite sequence a1, a2, a3, ..., an, each term after the firs 07 Oct 2025, 11:26
Kudos
Add Kudos
Bookmarks
Bookmark this Post
where does the 14 came from;im sorry im a beginner
Bunuel
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 \(a_5-a_2=12\), 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 \(a_n=2^{n-1}*a_1\) . So:
\(a_5=2^4*a_1\);
\(a_2=2*a_1\);

Given: \(a_5-a_2=2^4*a_1-2*a_1=12\) --> \(2^4*a_1-2*a_1=12\) --> \(a_1=\frac{12}{14}=\frac{6}{7}\).

Answer: E.

Hope it's clear.
Show more
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 23 Apr 2026
Posts: 109,785
Own Kudos:
810,869
 [2]
Given Kudos: 105,853
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 109,785
Kudos: 810,869
 [2]
In the infinite sequence a1, a2, a3, ..., an, each term after the firs 07 Oct 2025, 14:10
2
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Ranjansudhanshu
where does the 14 came from;im sorry im a beginner

Show more

\(2^4*a_1-2*a_1=12\)

\(16*a_1-2*a_1=12\)

\(14*a_1=12\)

\(a_1=\frac{12}{14}=\frac{6}{7}\).
Moderators:
Bunuel
Math Expert
109785 posts
Krunaal
Tuck School Moderator
853 posts