 It is currently 24 May 2020, 16:38 ### 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. # QOTD#8 The first term in a certain sequence is 1, the 2nd  Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS: Retired Moderator Joined: 07 Jun 2014
Posts: 4806
GRE 1: Q167 V156 WE: Business Development (Energy and Utilities)
Followers: 162

Kudos [?]: 2654  , given: 394

QOTD#8 The first term in a certain sequence is 1, the 2nd [#permalink]
1
KUDOS
Expert's post 00:00

Question Stats: 77% (01:57) correct 22% (01:27) wrong based on 35 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?

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 GRE Instructor Joined: 10 Apr 2015
Posts: 3244
Followers: 124

Kudos [?]: 3619  , given: 61

Re: QOTD#8 The first term in a certain sequence is 1, the 2nd [#permalink]
5
KUDOS
Expert's post
Explanation

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...

[Reveal] Spoiler:
3/2

RELATED VIDEOS

_________________

Brent Hanneson – Creator of greenlighttestprep.com  Intern Joined: 15 Dec 2016
Posts: 18
Followers: 0

Kudos [?]: 11  , given: 3

Re: QOTD#8 The first term in a certain sequence is 1, the 2nd [#permalink]
1
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.
Intern Joined: 12 Aug 2019
Posts: 2
Followers: 0

Kudos [?]: 0 , given: 1

Re: QOTD#8 The first term in a certain sequence is 1, the 2nd [#permalink]
This question is not clear to me, the above rule is applicable only for first 3rd number but in case of 4th number the result is not be 1.5, would you please elaborate the answer for 4th, 5th & 6th terms. GRE Instructor Joined: 10 Apr 2015
Posts: 3244
Followers: 124

Kudos [?]: 3619  , given: 61

Re: QOTD#8 The first term in a certain sequence is 1, the 2nd [#permalink]
4
KUDOS
Expert's post
Question: 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?

revengeoftheluddites wrote:
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?

That's not correct.
The question says "for all integers n ≥ 3, the nth term in the sequence is...."
So, the rule applies to the 3rd term, the 4th term, the 5th term, etc.
In fact the rule applies to all terms after term 1 and term 2.

In other words, the part that says "for all integers n ≥ 3, the nth term in the sequence is...." is not referring to the VALUE of the terms. It's referring to the term number (e.g., term 5, term 11, etc)

Does that help?

Cheers,
Brent
_________________

Brent Hanneson – Creator of greenlighttestprep.com Director  Joined: 22 Jun 2019
Posts: 522
Followers: 4

Kudos [?]: 98 , given: 161

Re: QOTD#8 The first term in a certain sequence is 1, the 2nd [#permalink] Re: QOTD#8 The first term in a certain sequence is 1, the 2nd   [#permalink] 12 Nov 2019, 00:10
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 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®.