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

It is currently 13 Nov 2019, 03:17

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

For the sequence a1, a2, a3 ... an, an is defined by an = an−1 + 3. If

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

Hide Tags

Find Similar Topics 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 59012
For the sequence a1, a2, a3 ... an, an is defined by an = an−1 + 3. If  [#permalink]

Show Tags

New post 04 Apr 2018, 22:10
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

86% (01:26) correct 14% (01:25) wrong based on 77 sessions

HideShow timer Statistics

Senior Manager
Senior Manager
User avatar
G
Joined: 31 May 2017
Posts: 334
GMAT ToolKit User Reviews Badge
Re: For the sequence a1, a2, a3 ... an, an is defined by an = an−1 + 3. If  [#permalink]

Show Tags

New post 05 Apr 2018, 20:26
1
The numbers are addition of 3 to each numbers from a2 to a15.

a12 = 33
a15 = 42
a15 - a12 = 42-33 = 9

Ans: C

Posted from my mobile device
_________________
Manager
Manager
avatar
G
Joined: 05 Feb 2016
Posts: 166
Location: India
Concentration: General Management, Marketing
WE: Information Technology (Computer Software)
GMAT ToolKit User CAT Tests
Re: For the sequence a1, a2, a3 ... an, an is defined by an = an−1 + 3. If  [#permalink]

Show Tags

New post 04 Apr 2018, 22:25
Bunuel wrote:
For the sequence \(a_1\), \(a_2\), \(a_3\) ... \(a_n\), \(an\) is defined by \(a_n = a_{n−1} + 3\). If \(a_1 = 0\), then what is \(a_{15} − a_{12}\)?

A. 3
B. 6
C. 9
D. 12
E. 15


\(a_{15} = a_{1} + 3*14\)
\(a_{12} = a_{1} + 3*11\)

\(a_{15} − a_{12}=9\)
Senior SC Moderator
avatar
V
Joined: 22 May 2016
Posts: 3648
For the sequence a1, a2, a3 ... an, an is defined by an = an−1 + 3. If  [#permalink]

Show Tags

New post 05 Apr 2018, 05:53
Bunuel wrote:
For the sequence \(a_1\), \(a_2\), \(a_3\) ... \(a_n\), \(an\) is defined by \(a_n = a_{n−1} + 3\). If \(a_1 = 0\), then what is \(a_{15} − a_{12}\)?

A. 3
B. 6
C. 9
D. 12
E. 15

The sequence is defined by
\(a_n = a_{n−1} + 3\). If the way to solve is not apparent, list a few terms.

\(a_1 = 0\)
\(a_2 = a_1 + 3 = (0 + 3) = 3\)
\(a_3 = a_2 + 3 = 6\)
\(a_4 = a_3 + 3 = 9\)
\(a_5 = 12\)


There are a lot of ways to handle this pattern.
You can extrapolate, for example, from the number of multiples of 3 between three terms, or rewrite the definition.*

Extrapolate from \(a_1\) to \(a_4\) and \(a_2\) to \(a_5\):
The difference between any three terms is 9
From \(a_{12}\) to \(a_{15}\) there are 3 terms
The difference between those terms is 9

Answer C

Rewrite the definition
Express the values above as [something] + added 3s;[something] is 0 = \(a_1\)

\(a_1 = 0\)
\(a_2 = 3 = (0+3)\)
\(a_3 = 6 = (0+3+3)\)
\(a_4 = 9 = (0)+(3+3+3)\)
\(a_5 = 12 = (0)+(3+3+3+3) =
(a_1 + (4)(3))\)


Each term's multiple of 3 is one fewer than the subscript. Rewritten definition of the AP:
\(a_{n} = a_1 + (n-1)d\)
\(a_{n} = a_1 + (n-1)3\)

\(a_{12} = 0 + (11*3) = 33\)
\(a_{15} = 0 + (14*3) = 42\)
\(a_{15} - a_{12} = (42-33) = 9\)


Answer C

*If the pattern does not strike, list terms \(a_1\) to \(a_{15}\)
\(0,3,6,9,12,15,18,21,24,27,30,\)
\((33 = a_{12}),36,39,(42 = a_{15})\)
\(a_{15} - a_{12} = (42 - 33) = 9\)

_________________
SC Butler has resumed! Get two SC questions to practice, whose links you can find by date, here.

Never doubt that a small group of thoughtful, committed citizens can change the world; indeed, it's the only thing that ever has -- Margaret Mead
GMAT Club Bot
For the sequence a1, a2, a3 ... an, an is defined by an = an−1 + 3. If   [#permalink] 05 Apr 2018, 05:53
Display posts from previous: Sort by

For the sequence a1, a2, a3 ... an, an is defined by an = an−1 + 3. If

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





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