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.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

In a sequence of 12 numbers, each term, except for the first [#permalink]

Show Tags

03 Nov 2012, 18:36

12

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

55% (hard)

Question Stats:

61% (02:24) correct
39% (01:50) wrong based on 290 sessions

HideShow timer Statistics

In a sequence of 12 numbers, each term, except for the first one, is 12^11 less than the previous term. If the greatest term in the sequence is 12^12, what is the smallest term in the sequence?

Remember the formula for an arithmetic sequence: An = A1+(n-1)d

Thus, A12 = A1+(12-1)d

Where d is the difference between each pairs of consecutive terms. Since each term is 1211 less than the previous term, d=-1211Click individual answer choices for specific explanations.

From what I undersltand the formula for an arithmetic sequence represents

"some-number-in-the-sequence" = first-number-in-sequence + (the-place-of-that-number - 1) x the-difference-of-each-#-in-the-sequence

I'm not exactly sure how that formula fits into the question, could someone help me to understand?

Re: In a sequence of 12 numbers, each term, except for the first [#permalink]

Show Tags

03 Nov 2012, 21:24

4

This post received KUDOS

2

This post was BOOKMARKED

anon1 wrote:

In a sequence of 12 numbers, each term, except for the first one, is 12^11 less than the previous term. If the greatest term in the sequence is 12^12, what is the smallest term in the sequence?

−12^11 0 12^11 11·12^11 12^12

In this question, there are total 12 terms. and "greatest" term is 12^12. Each term is 12^11 less than previous one. What does this signify? This shows it is an AP - a decreasing one. (Notice "Each term is 12^11 less than previous one')

Therefore, 12^12 is the first term of the AP and -12^11 is the difference between successive terms, the smallest term should be the last one.

Last term = First term + (n-1)*d therefore, Last term = 12^12 + 11*(-12^11) => Last term = 12^12 - 11*12^11 => Last term = 12^11 (12-11) = 12^11 Which is the smallest term.

Re: In a sequence of 12 numbers, each term, except for the first [#permalink]

Show Tags

05 Nov 2012, 04:00

bhavinshah5685 wrote:

hi, I am not able to understand one basic...

How can we infer that 12^12 is the first term or the last term in the sequence given in question?? Is it trial and error...???

Thanks in advance..

Question says:

1)each term, except for the first one, is 12^11 less than the previous term => decreasing AP 2)greatest term in the sequence is 12^12 Which term is greatest in a decreasing AP? First one!

Re: In a sequence of 12 numbers, each term, except for the first [#permalink]

Show Tags

05 Nov 2012, 15:19

I am confused.... "except for the first one," what does this phrase in the question has to say..... remaining sequence is fine... but they never mentioned this series to be a AP series.... what if first term is 12^9? this will be the lowest term right?

Re: In a sequence of 12 numbers, each term, except for the first [#permalink]

Show Tags

05 Nov 2012, 15:55

In a sequence of 12 numbers, each term, except for the first one, is 12^11 less than the previous term. If the greatest term in the sequence is 12^12, what is the smallest term in the sequence?

The above are the 12 numbers represented by underscores, and the numbers beneath represent their position in the sequence.

The question only mentions "except for the first one" because it wants to state again that there is nothing before the first number. It is a little redundant but the question wants to make itself clear.

The first number can't be 12^9 because it tells you that the numbers get smaller and 12^12 is the biggest number. Therefore 12^12 is the first number.

Re: In a sequence of 12 numbers, each term, except for the first [#permalink]

Show Tags

05 Nov 2012, 23:33

1

This post received KUDOS

anon1 wrote:

Ohhhhh, I see.

I didn't realize that APs could decreasing...

I looked at the question as if 12^12 was the last number in the sequence and that the first (the smallest) was unknown. Thank you as always VIPS

Just a heads up... Although an A.P could be a decreasing one, the one in the question is not. The last term is 12^12 and every term before its is lesser than 12^12. So the first term is 12^11 and last term is 12^12. So the A.P is in fact an increasing one.

Kudos Please... If my post helped.
_________________

Did you find this post helpful?... Please let me know through the Kudos button.

Re: In a sequence of 12 numbers, each term, except for the first [#permalink]

Show Tags

06 Nov 2012, 00:12

MacFauz wrote:

Just a heads up... Although an A.P could be a decreasing one, the one in the question is not. The last term is 12^12 and every term before its is lesser than 12^12. So the first term is 12^11 and last term is 12^12. So the A.P is in fact an increasing one.

Kudos Please... If my post helped.

And how do you exactly interpret this?

question clearly says: "each term is 12^11 less than the previous term" . This could be true "ONLY IF" its a decreasing AP. Unless you are counting from right to left?

for example in 10, 8, 6, 4... each term is 2 less than the previous term
_________________

Re: In a sequence of 12 numbers, each term, except for the first [#permalink]

Show Tags

06 Nov 2012, 01:00

Haha... Yes.. I was considering the A.P as 12^11, 12^11+12^11,12^11+12^11+12^11 and so on with ther 12th term being 12^11 + 11*12^12... .. I could be wrong though...
_________________

Did you find this post helpful?... Please let me know through the Kudos button.

Re: In a sequence of 12 numbers, each term, except for the first [#permalink]

Show Tags

23 Aug 2013, 23:40

3

This post received KUDOS

In a sequence of 12 numbers, each term, except for the first one, is 12^11 less than the previous term. If the greatest term in the sequence is 12^12, what is the smallest term in the sequence?

A. −12^11 B. 0 C. 12^11 D. 11·12^11 E. 12^12

common Difference= 12^11 Last term = 12^12 Last term = First Term + last Term X common difference. 12^11= First term + 12^12 X 12^11 First term=12^11 - 12^12 X 12^11 First term=12^11(12-11) First term=12^11 OA-C

Re: In a sequence of 12 numbers, each term, except for the first [#permalink]

Show Tags

24 Sep 2013, 16:48

4

This post received KUDOS

1

This post was BOOKMARKED

Points to note in this problem: 1) We have 12 terms 2) Greatest value is 12^12 3) Every other value decreases by 12^11 If we can notice that 12 * 12^11 = 12^12, we can conclude that the smallest value must be 12^11 without doing any math.

Here's the underlying concept: 3^5 + 3^5 + 3^5 = 3*3^5 = 3^6 OR 3^6 - 3^5 - 3^5 = 3^5. --> So if this were a set of "3" terms, it could be {3(3^5), 2(3^5), 3^5} OR {3^6, 2*3^5, 3^5}

Therefore, in this case, 12^11 + 12^11 +...(12 times) = 12*12^11 = 12^12. OR 12^12 - 11 ( 12^11) = 12^11. So the smallest value must be 12^11.

Re: In a sequence of 12 numbers, each term, except for the first [#permalink]

Show Tags

22 Jun 2015, 12:09

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

Re: In a sequence of 12 numbers, each term, except for the first [#permalink]

Show Tags

22 Jun 2015, 12:21

Vips0000 wrote:

anon1 wrote:

In a sequence of 12 numbers, each term, except for the first one, is 12^11 less than the previous term. If the greatest term in the sequence is 12^12, what is the smallest term in the sequence?

−12^11 0 12^11 11·12^11 12^12

In this question, there are total 12 terms. and "greatest" term is 12^12. Each term is 12^11 less than previous one. What does this signify? This shows it is an AP - a decreasing one. (Notice "Each term is 12^11 less than previous one')

Therefore, 12^12 is the first term of the AP and -12^11 is the difference between successive terms, the smallest term should be the last one.

Last term = First term + (n-1)*d therefore, Last term = 12^12 + 11*(-12^11) => Last term = 12^12 - 11*12^11 => Last term = 12^11 (12-11) = 12^11 Which is the smallest term.

Hence Ans C it is.

Please anyone help me how to get from red to blue in the equality above. Thanks!
_________________

Saving was yesterday, heat up the gmatclub.forum's sentiment by spending KUDOS!

PS Please send me PM if I do not respond to your question within 24 hours.

In a sequence of 12 numbers, each term, except for the first one, is 12^11 less than the previous term. If the greatest term in the sequence is 12^12, what is the smallest term in the sequence?

−12^11 0 12^11 11·12^11 12^12

In this question, there are total 12 terms. and "greatest" term is 12^12. Each term is 12^11 less than previous one. What does this signify? This shows it is an AP - a decreasing one. (Notice "Each term is 12^11 less than previous one')

Therefore, 12^12 is the first term of the AP and -12^11 is the difference between successive terms, the smallest term should be the last one.

Last term = First term + (n-1)*d therefore, Last term = 12^12 + 11*(-12^11) => Last term = 12^12 - 11*12^11 => Last term = 12^11 (12-11) = 12^11 Which is the smallest term.

Hence Ans C it is.

Please anyone help me how to get from red to blue in the equality above. Thanks!

Re: In a sequence of 12 numbers, each term, except for the first [#permalink]

Show Tags

21 Sep 2016, 17:56

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

Its been long time coming. I have always been passionate about poetry. It’s my way of expressing my feelings and emotions. And i feel a person can convey...

Written by Scottish historian Niall Ferguson , the book is subtitled “A Financial History of the World”. There is also a long documentary of the same name that the...

Post-MBA I became very intrigued by how senior leaders navigated their career progression. It was also at this time that I realized I learned nothing about this during my...