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

 It is currently 18 Oct 2019, 04:11 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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  {an} is a sequence satisfying an+2 = an+1 + an. If a1 = a4 = 2, what i

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

Hide Tags

Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8017
GMAT 1: 760 Q51 V42 GPA: 3.82
{an} is a sequence satisfying an+2 = an+1 + an. If a1 = a4 = 2, what i  [#permalink]

Show Tags

1
1 00:00

Difficulty:   25% (medium)

Question Stats: 81% (02:29) correct 19% (02:50) wrong based on 35 sessions

HideShow timer Statistics

[GMAT math practice question]

{an} is a sequence satisfying an+2 = an+1 + an. If a1 = a4 = 2, what is the value of a7?

A. 10
B. 12
C. 14
D. 15
E. 16

_________________
Senior Manager  S
Joined: 12 Sep 2017
Posts: 302
{an} is a sequence satisfying an+2 = an+1 + an. If a1 = a4 = 2, what i  [#permalink]

Show Tags

1
An+2 = An+1 + An
An = An+2 - An+1

A1 = 2
A2 = ?
A3 = ?
A4 = 2

Sum of A2 + A3 must be 2 when A2 = An. (An+2 = An4 = An+1 = An3 + An = A2)

Subtraction of A3 - A2 must be 2 when An = An1. ((An = An1 = 2) = (An+2 = An3) - (An+1 = An2))

I took the values 2 and 0.

Given that A1 = 2 is positive, then A2 has to be 0 and A3 has to be 2 so...

A1 = A3 - A2 = 2 - 0 = 2 = A1

After that just sum:

A5 = A3 + A4 = 4
A6 = A4 + A5 = 6
A7 = A5 + A6 = 10

A
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8017
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: {an} is a sequence satisfying an+2 = an+1 + an. If a1 = a4 = 2, what i  [#permalink]

Show Tags

=>

a3 = a2 + a1 = a2 + 2.
a4 = a3 + a2 = a2 + (a2 + 2) = 2a2 + 2 = 2.
Thus, a2 = 0 and a3 = 2.
Therefore,
a5 = a4 + a3 = 2 + 2 = 4,
a6 = a5 + a4 = 4 + 2 = 6,
and
a7 = a6 + a5 = 6 + 4 = 10.

Therefore, the answer is A.
_________________ Re: {an} is a sequence satisfying an+2 = an+1 + an. If a1 = a4 = 2, what i   [#permalink] 01 Feb 2019, 02:50
Display posts from previous: Sort by

{an} is a sequence satisfying an+2 = an+1 + an. If a1 = a4 = 2, what i

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

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