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

 It is currently 14 Aug 2018, 22:04

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

M23-07

Author Message
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 47898

Show Tags

16 Sep 2014, 01:18
00:00

Difficulty:

15% (low)

Question Stats:

85% (01:37) correct 15% (01:15) wrong based on 99 sessions

HideShow timer Statistics

The sequence $$a_1$$, $$a_2$$, $$a_3$$, ... , $$a_n$$, ... is such that $$a_n=a_{n-1}+a_{n-2}$$ for all $$n \ge 3$$. If $$a_1 = 3$$ and $$a_5 = 6$$, what is the value of $$a_2$$ ?

A. -3
B. -1
C. 0
D. 2
E. 3

_________________
Math Expert
Joined: 02 Sep 2009
Posts: 47898

Show Tags

16 Sep 2014, 01:18
1
Official Solution:

The sequence $$a_1$$, $$a_2$$, $$a_3$$, ... , $$a_n$$, ... is such that $$a_n=a_{n-1}+a_{n-2}$$ for all $$n \ge 3$$. If $$a_1 = 3$$ and $$a_5 = 6$$, what is the value of $$a_2$$ ?

A. -3
B. -1
C. 0
D. 2
E. 3

Since given that $$a_n=a_{n-1}+a_{n-2}$$, then:

$$a_5=a_4+a_3=(a_3+a_2)+(a_2+a_1)=((a_2+a_1)+a_2)+(a_2+a_1)=3*a_2+2*a_1$$.

So, we have that $$a_5=3*a_2+2*a_1$$, or $$6=3*a_2+2*3$$, which gives $$a_2=0$$.

_________________
Intern
Joined: 24 Feb 2017
Posts: 37

Show Tags

27 Apr 2017, 22:43
i didn't get it !
how can you solve this?
Manager
Joined: 02 May 2016
Posts: 82
Location: India
Concentration: Entrepreneurship
GRE 1: Q163 V154
WE: Information Technology (Computer Software)

Show Tags

26 May 2017, 07:32
1
mkumar26 wrote:
i didn't get it !
how can you solve this?

Nth term = (N-1)th term + (n-2)th term

Just substitute the values:

a1=3
a2=x
a3=a2+a1 =x+3
a4=a3+a2 =x+3+x =2x+3
a5=a4+a3 =2x+3+x+3 = 3x+6

now a5=6, so 3x+6=6 ~ 3x=0 ~ x=0.
Hence, a2=x=0.

This is lengthy process though!
Intern
Joined: 02 Jun 2015
Posts: 18
Location: United States

Show Tags

14 Mar 2018, 14:56
I believe the best way to solve this question is using "TEST THE ANSWERS" or "BACKSOLVING".

Let's use "C" because zero is an easy number to work with.

An= An-1 + An-2

Where A1=3 and A5=6

If A2 = 0

A3= A2 + A1
A3= 0 + 3
A3 = 3

A4= A3 + A2
A4 = 3 + 0
A4 = 3

A5= A4 + A3
A5= 3 + 3
A5=6 That's a match

I hope it helps!!
Thanks! Ale
Re: M23-07 &nbs [#permalink] 14 Mar 2018, 14:56
Display posts from previous: Sort by

M23-07

Moderators: chetan2u, Bunuel

Events & Promotions

 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®.