It is currently 17 Nov 2018, 15:13
My Tests

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.

QOTD#8 The first term in a certain sequence is 1, the 2nd

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 07 Jun 2014
Posts: 4710
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 91

Kudos [?]: 1613 [0], given: 375

CAT Tests
QOTD#8 The first term in a certain sequence is 1, the 2nd [#permalink] New post 12 Sep 2016, 11:07
Expert's post
00:00

Question Stats:

71% (01:49) correct 28% (01:39) wrong based on 7 sessions
The first term in a certain sequence is 1, the 2nd term in the sequence is 2, and, for all integers n ≥ 3, the nth term in the sequence is the average (arithmetic mean) of the first n – 1 terms in the sequence. What is the value of the 6th term in the sequence?

Give your answer as a fraction.

Practice Questions
Question: 21
Page: 208-209


[Reveal] Spoiler: OA
3/2

_________________

Sandy
If you found this post useful, please let me know by pressing the Kudos Button

Try our free Online GRE Test

GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 07 Jun 2014
Posts: 4710
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 91

Kudos [?]: 1613 [0], given: 375

CAT Tests
Re: QOTD#8 The first term in a certain sequence is 1, the 2nd [#permalink] New post 12 Sep 2016, 11:16
Expert's post
Explanation

For all integers n ≥ 3, the nth term in the sequence is the average of the first n – 1 terms in the sequence.

The 3rd term, which is the average of the first 2 terms, is \(\frac{(1+2)}{2}\), or 1.5.

The 4th term, which is the average of the first 3 terms, is \(\frac{(1+2+1.5)}{3}\), or 1.5.

Similarly, the 5th term is \(\frac{(1+2+1.5+1.5)}{4}= \frac{6}{4}=1.5\), and the 6th term is \(\frac{(1+2+1.5+1.5+1.5)}{5}\) or 1.5. Since you must give your answer as a fraction, the correct
answer is \(\frac{3}{2}\).
_________________

Sandy
If you found this post useful, please let me know by pressing the Kudos Button

Try our free Online GRE Test

3 KUDOS received
GRE Instructor
User avatar
Joined: 10 Apr 2015
Posts: 1177
Followers: 44

Kudos [?]: 1053 [3] , given: 6

CAT Tests
Re: QOTD#8 The first term in a certain sequence is 1, the 2nd [#permalink] New post 18 Nov 2016, 06:29
3
This post received
KUDOS
Expert's post
sandy wrote:
The first term in a certain sequence is 1, the 2nd term in the sequence is 2, and, for all integers n ≥ 3, the nth term in the sequence is the average (arithmetic mean) of the first n – 1 terms in the sequence. What is the value of the 6th term in the sequence?

Give your answer as a fraction.


Before I answer this question, consider the following example:
Let's say that set T consists of {1, 2, 4, 5}. The AVERAGE = 3
What happens if we add 3 to get: {1, 2, 3, 4, 5}?
The average stays at 3 BECAUSE we added a value that was already the average of the original 4 values.

The same applies to this question:
term1 = 1
term2 = 2
term3 = (1+2)/2 = 1.5

term4: term 4 equals the AVERAGE of terms 1, 2 and 3. Notice that the AVERAGE of terms 1 and 2 is 1.5.
So, to find term4, we take terms 1 and 2 (which we already know has an average of 1.5) and we add to those values another 1.5 (which is term3), then the average won't change.
So, term4 = 1.5

And so on....
So, term6 = 1.5 and term7 = 1.5 and term8 = 1.5, and so on...

Answer:
[Reveal] Spoiler:
3/2


RELATED VIDEOS



_________________

Brent Hanneson – Creator of greenlighttestprep.com
Image
Sign up for our free GRE Question of the Day emails

1 KUDOS received
Intern
Intern
Joined: 15 Dec 2016
Posts: 18
Followers: 0

Kudos [?]: 6 [1] , given: 3

Re: QOTD#8 The first term in a certain sequence is 1, the 2nd [#permalink] New post 16 Dec 2016, 00:14
1
This post received
KUDOS
Can you please clarify. The question says "for all integers where n is equal to or greater than 3" the rule applies. If you take the third term, you can't apply that rule unless the third term is 3, right? If you take the average of 1 and 2, and average them, then you are following the rule but you are doing so for an integer that is less than the rule states, so it's a paradox. By my reading of the question, the correct answer should be 1,2,3, then you apply the rule, so the average of 1+2+3 is 3, then the average of 1+2+3+3 is 4.5, then the average of 1+2+3+3+4.5 is 6.75, and so on.
Re: QOTD#8 The first term in a certain sequence is 1, the 2nd   [#permalink] 16 Dec 2016, 00:14
Display posts from previous: Sort by

QOTD#8 The first term in a certain sequence is 1, the 2nd

  Question banks Downloads My Bookmarks Reviews Important topics  


cron

GRE Prep Club Forum Home| About| Terms and Conditions and Privacy Policy| GRE Prep Club Rules| Contact

Powered by phpBB © phpBB Group

Kindly note that the GRE® test is a registered trademark of the Educational Testing Service®, and this site has neither been reviewed nor endorsed by ETS®.