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.

What do you need to know to get accepted to a Master's in Finance program? This free guide will provide you with the clear, concrete, actionable advice that you need to go from MFiN applicant to MFiN student.

Economist GRE Tutor’s plans all come with a set of practice exams that mirror the official GRE test. Our academic team worked hard to make sure that the practice tests are the closest experience you can get to the real GRE exam.

Within each of the 16 learning modules (Geometry, Statistics, Sentence Equivalence, etc.) that comprise the course, you'll find plenty of free videos to help you make an informed purchase. I also have 4 modules in which all of the videos are free.

Magoosh is excited to offer you a free GRE practice test with video answers and explanations. If you’re thinking about taking the GRE or want to see how effective your GRE test prep has been, pinpoint your strengths and weaknesses with this quiz!

QOTD#8 The first term in a certain sequence is 1, the 2nd [#permalink]
12 Sep 2016, 11:07

1

This post received KUDOS

Expert's post

00:00

Question Stats:

72% (01:29) correct
27% (01:27) wrong based on 18 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?

Re: QOTD#8 The first term in a certain sequence is 1, the 2nd [#permalink]
18 Nov 2016, 06:29

5

This post received 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...

Re: QOTD#8 The first term in a certain sequence is 1, the 2nd [#permalink]
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]
14 Aug 2019, 00:44

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.

Re: QOTD#8 The first term in a certain sequence is 1, the 2nd [#permalink]
14 Aug 2019, 04:37

4

This post received 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 Array[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 Sign up for my free GRE Question of the Dayemails