Check GMAT Club Decision Tracker for the Latest School Decision Releases https://gmatclub.com/AppTrack

 It is currently 28 May 2017, 09:04

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# The sequence a(1), a(2), ..., a(n), ... is such that

Author Message
TAGS:

### Hide Tags

Intern
Joined: 17 Oct 2011
Posts: 23
Location: Taiwan
GMAT 1: 590 Q39 V34
GMAT 2: 680 Q47 V35
Followers: 0

Kudos [?]: 60 [1] , given: 10

The sequence a(1), a(2), ..., a(n), ... is such that [#permalink]

### Show Tags

02 Mar 2012, 21:12
1
KUDOS
2
This post was
BOOKMARKED
00:00

Difficulty:

25% (medium)

Question Stats:

73% (02:25) correct 27% (02:05) wrong based on 298 sessions

### HideShow timer Statistics

The sequence a(1), a(2), …, a(n), … is such that a(n)=4a(n–1) –3 for all integers n>1. If a(3)=x, then a(1)=?

A. 4x–3
B. 16x–15
C. (x+3)/4
D. (x+3)/16
E. (x+15)/16
[Reveal] Spoiler: OA
Math Expert
Joined: 02 Sep 2009
Posts: 38985
Followers: 7748

Kudos [?]: 106435 [0], given: 11626

Re: If a(3)=x, then a(1)=? [#permalink]

### Show Tags

02 Mar 2012, 21:29
The sequence $$a_1$$, $$a_2$$, …, $$a_n$$, … is such that $$a_n=4a_{n-1}-3$$ for all integers n>1. If $$a_3$$=x, then $$a_1=$$?
A. 4x–3
B. 16x–15
C. (x+3)/4
D. (x+3)/16
E. (x+15)/16

Since, $$a_n=4a_{n-1}-3$$ then $$a_3=4a_{2}-3$$ --> $$x=4a_{2}-3$$ --> $$a_2=\frac{x+3}{4}$$.

Similarly, $$a_2=4a_{1}-3$$ --> $$\frac{x+3}{4}=4a_{1}-3$$ --> $$a_1=\frac{x+15}{16}$$.

Or substitute the value for $$x$$, say $$x=5$$, then $$a_3=5=4a_{2}-3$$ --> $$a_2=2$$ --> $$a_2=2=4a_{1}-3$$ --> $$a_1=\frac{5}{4}$$. Now, just plug $$x=5$$ in the answer choices and see which one yields $$\frac{5}{4}$$: only E.

Note that for plug-in method it might happen that for some particular number(s) more than one option may give "correct" answer. In this case just pick some other numbers and check again these "correct" options only. For example if you pick $$x=1$$ then you get three "correct" options A, C and E. Generally -1, 0, and 1 are not good choices for plug-in method.

Hope it helps.
_________________
Intern
Joined: 28 Sep 2011
Posts: 34
Location: India
WE: Consulting (Computer Software)
Followers: 1

Kudos [?]: 16 [0], given: 18

Re: If a(3)=x, then a(1)=? [#permalink]

### Show Tags

02 Mar 2012, 21:34
The sequence a(1), a(2), …, a(n), … is such that a(n)=4a(n–1) –3 for all integers n>1. If a(3)=x, then a(1)=?

My Line of thought:
1. What is given to me a(3)=x, and formula.
2. I need to express a(1) from known.
3. a(n) can be expressed as a(n-1) means it can be expressed by any of the predecessor or successor.
as a(n-1) can be expressed as a(n-2)....hence a(n) can be expressed as a(n-2) and vice versa
4. a(3) = 4a(2)-3 , (n=3)>1
= 4 [4a(1)-3]-3 , (n=2)>1
=16a(1)-12-3
x = 16a(1)-15
(x+15)/16 = a(1) == Ans E
_________________

Kudos if you like the post!!!

Math Expert
Joined: 02 Sep 2009
Posts: 38985
Followers: 7748

Kudos [?]: 106435 [0], given: 11626

Re: The sequence a(1), a(2), ..., a(n), ... is such that [#permalink]

### Show Tags

04 Jun 2013, 05:54
Bumping for review and further discussion*. Get a kudos point for an alternative solution!

*New project from GMAT Club!!! Check HERE
_________________
Manager
Joined: 28 Feb 2012
Posts: 115
GPA: 3.9
WE: Marketing (Other)
Followers: 0

Kudos [?]: 45 [0], given: 17

Re: The sequence a(1), a(2), ..., a(n), ... is such that [#permalink]

### Show Tags

05 Jun 2013, 07:01
The sequence a(1), a(2), …, a(n), … is such that a(n)=4a(n–1) –3 for all integers n>1. If a(3)=x, then a(1)=?

A. 4x–3
B. 16x–15
C. (x+3)/4
D. (x+3)/16
E. (x+15)/16

I love such questions!

Since we know a(3) we can find a(2), if we can find a(2) we can find a(1). a(3)=4a(2)-3 ---> x=4a(2)-3 ---> a(2)=(x+3)/4

a(2)=4a(1)-3 ---> (x+3)/4=4a(1)-3 ---> 4a(1)=(x+15)/4 ---> a(1)=(x+15)/16 The answer is E.
_________________

If you found my post useful and/or interesting - you are welcome to give kudos!

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 15497
Followers: 651

Kudos [?]: 210 [0], given: 0

Re: The sequence a(1), a(2), ..., a(n), ... is such that [#permalink]

### Show Tags

22 Sep 2016, 19:30
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: The sequence a(1), a(2), ..., a(n), ... is such that   [#permalink] 22 Sep 2016, 19:30
Similar topics Replies Last post
Similar
Topics:
38 A sequence of numbers a1, a2, a3,…. is defined as follows: a1 = 3, a2 5 06 Aug 2016, 06:03
21 The sequence a1, a2, a3, ... ,an, ... is such that an = an-1 16 18 Apr 2017, 22:27
28 The infinite sequence a1, a2, …, an, … is such that a1=2 12 02 Mar 2017, 18:13
21 The infinite sequence a1, a2,...,an is defined such that an 15 02 Dec 2016, 02:09
11 The sequence a1, a2, … , a n, … is such that an = 2an-1 - x 13 21 Jan 2017, 03:28
Display posts from previous: Sort by