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

 It is currently 16 Aug 2018, 12:48

### 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

# In the sequence 1, 2, 4, .... an, every nth term for n > 1 is created

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 47946
In the sequence 1, 2, 4, .... an, every nth term for n > 1 is created  [#permalink]

### Show Tags

28 Feb 2016, 09:17
1
4
00:00

Difficulty:

55% (hard)

Question Stats:

60% (00:58) correct 40% (01:00) wrong based on 234 sessions

### HideShow timer Statistics

In the sequence 1, 2, 4, .... an, every nth term for n > 1 is created by the equation $$a_n=a_{(n−1)}∗2$$. By what percent is the 11th term greater than the 9th term in this sequence?

A. 100%
B. 200%
C. 300%
D. 400%
E. 800%

_________________
Manager
Joined: 25 Dec 2012
Posts: 123
Re: In the sequence 1, 2, 4, .... an, every nth term for n > 1 is created  [#permalink]

### Show Tags

28 Feb 2016, 11:46
Bunuel wrote:
In the sequence 1, 2, 4, .... an, every nth term for n > 1 is created by the equation $$a_n=a_{(n−1)}∗2$$. By what percent is the 11th term greater than the 9th term in this sequence?

A. 100%
B. 200%
C. 300%
D. 400%
E. 800%

Since its a GP, the property will hold true for the entire sequence. For instance the percent difference between 1st term and 3rd term is equal to the question stem.

Hence 4/1 = 4 which is 400%

IMO D.
BSchool Forum Moderator
Joined: 12 Aug 2015
Posts: 2649
GRE 1: Q169 V154
Re: In the sequence 1, 2, 4, .... an, every nth term for n > 1 is created  [#permalink]

### Show Tags

09 Mar 2016, 04:21
2
Manager
Joined: 14 Oct 2012
Posts: 175
Re: In the sequence 1, 2, 4, .... an, every nth term for n > 1 is created  [#permalink]

### Show Tags

01 Sep 2016, 12:01
1, 2, 4, 8, 16, 32, 64, 128, 256(9th term), 512, 1024(11th term)
Therefore, [(2^10 – 2^8)/2^8]*100 = [2^2 – 1]*100 = 300%
SC Moderator
Joined: 22 May 2016
Posts: 1903
In the sequence 1, 2, 4, .... an, every nth term for n > 1 is created  [#permalink]

### Show Tags

08 Oct 2017, 06:42
1
Bunuel wrote:
In the sequence 1, 2, 4, .... an, every nth term for n > 1 is created by the equation $$a_n=a_{(n−1)}∗2$$. By what percent is the 11th term greater than the 9th term in this sequence?

A. 100%
B. 200%
C. 300%
D. 400%
E. 800%

$$a_1 = 1, a_2 = 2, a_3 = 4$$

Using $$a_n=a_{(n−1)}∗2$$

$$a_1 = 1$$
$$a_2 = 2$$
$$a_3 = 4 = (2 * 2)$$
$$a_4 = 8 = (2 * 2 * 2)$$
$$a_5 =16 = (2 * 2 * 2 * 2)$$
$$a_6=32=(2 * 2 * 2 * 2*2)$$

By definition, a geometric sequence has a common ratio.

The geometric expansion from $$a_2$$ to $$a_4$$ has the same ratio as the geometric expansion from $$a_{212}$$ to $$a_{214}$$, or the expansion between any two terms, 9$$^{th}$$ and 11$$^{th}$$ included.

In other words, $$a_{n+2}$$ will be the same percent greater than $$a_{n}$$ no matter which terms you choose.

So: $$a_4$$ is what percent greater than $$a_2$$?

Percent increase = $$\frac{New-Old}{Old} * 100$$

$$\frac{8 - 2}{2} =\frac{6}{2} * 100$$ = 300 percent

_________________

In the depths of winter, I finally learned
that within me there lay an invincible summer.

Intern
Joined: 11 Jun 2017
Posts: 31
Re: In the sequence 1, 2, 4, .... an, every nth term for n > 1 is created  [#permalink]

### Show Tags

08 Oct 2017, 10:53
KEY WORD: Greater than...
Intern
Joined: 07 Aug 2017
Posts: 4
Re: In the sequence 1, 2, 4, .... an, every nth term for n > 1 is created  [#permalink]

### Show Tags

11 Oct 2017, 14:23
I would just say that every GM sequence within a GM sequence holds the same percentage difference - so difference between first and third term is same as the difference between 9th and 11th term
--> therefore 300%
Re: In the sequence 1, 2, 4, .... an, every nth term for n > 1 is created &nbs [#permalink] 11 Oct 2017, 14:23
Display posts from previous: Sort by

# 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®.