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# In the Sequence x0, x1, x2, ..., xn, each term from x1 to xk

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In the Sequence x0, x1, x2, ..., xn, each term from x1 to xk [#permalink]

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05 Mar 2014, 02:20
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The Official Guide For GMAT® Quantitative Review, 2ND Edition

In the sequence $$x_0, \ x_1, \ x_2, \ ... \ x_n$$, each term from $$x_1$$ to $$x_k$$ is 3 greater than the previous term, and each term from $$x_{k+1}$$ to $$x_n$$ is 3 less than the previous term, where $$n$$ and $$k$$ are positive integers and $$k<n$$. If $$x_0=x_n=0$$ and if $$x_k=15$$, what is the value of $$n$$?

(A) 5
(B) 6
(C) 9
(D) 10
(E) 15

Problem Solving
Question: 131
Category: Algebra Sequences
Page: 78
Difficulty: 600

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Re: In the Sequence x0, x1, x2, ..., xn, each term from x1 to xk [#permalink]

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05 Mar 2014, 02:20
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SOLUTION

In the sequence $$x_0, \ x_1, \ x_2, \ ... \ x_n$$, each term from $$x_1$$ to $$x_k$$ is 3 greater than the previous term, and each term from $$x_{k+1}$$ to $$x_n$$ is 3 less than the previous term, where $$n$$ and $$k$$ are positive integers and $$k<n$$. If $$x_0=x_n=0$$ and if $$x_k=15$$, what is the value of $$n$$?

(A) 5
(B) 6
(C) 9
(D) 10
(E) 15

Probably the easiest way will be to write down all the terms in the sequence from $$x_0=0$$ to $$x_n=0$$. Note that each term from from $$x_0=0$$ to $$x_k=15$$ is 3 greater than the previous and each term from $$x_{k+1}$$ to $$x_n$$ is 3 less than the previous term:

So we'll have: $$x_0=0$$, 3, 6, 9, 12, $$x_k=15$$, 12, 9, 6, 3, $$x_n=0$$. So we have 11 terms from $$x_0$$ to $$x_n$$ thus $$n=10$$.

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Re: In the Sequence x0, x1, x2, ..., xn, each term from x1 to xk [#permalink]

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05 Mar 2014, 20:25
1

Series will be formed as below starting from x0 = 0 & ending up with x10 = 0

xk = 15

0, 3, 6, 9, 12, 15, 12, 9, 6, 3, 0
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Posts: 46264
Re: In the Sequence x0, x1, x2, ..., xn, each term from x1 to xk [#permalink]

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08 Mar 2014, 12:40
SOLUTION

In the sequence $$x_0, \ x_1, \ x_2, \ ... \ x_n$$, each term from $$x_1$$ to $$x_k$$ is 3 greater than the previous term, and each term from $$x_{k+1}$$ to $$x_n$$ is 3 less than the previous term, where $$n$$ and $$k$$ are positive integers and $$k<n$$. If $$x_0=x_n=0$$ and if $$x_k=15$$, what is the value of $$n$$?

(A) 5
(B) 6
(C) 9
(D) 10
(E) 15

Probably the easiest way will be to write down all the terms in the sequence from $$x_0=0$$ to $$x_n=0$$. Note that each term from from $$x_0=0$$ to $$x_k=15$$ is 3 greater than the previous and each term from $$x_{k+1}$$ to $$x_n$$ is 3 less than the previous term:

So we'll have: $$x_0=0$$, 3, 6, 9, 12, $$x_k=15$$, 12, 9, 6, 3, $$x_n=0$$. So we have 11 terms from $$x_0$$ to $$x_n$$ thus $$n=10$$.

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Re: In the Sequence x0, x1, x2, ..., xn, each term from x1 to xk [#permalink]

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26 Jul 2014, 22:17
Bunuel,

If the total terms ins sequence are 11, how is the no of terms n 10? Can you please explain? Thanks in advance.
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Posts: 46264
In the Sequence x0, x1, x2, ..., xn, each term from x1 to xk [#permalink]

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27 Jul 2014, 03:25
1
sri30kanth wrote:
Bunuel,

If the total terms ins sequence are 11, how is the no of terms n 10? Can you please explain? Thanks in advance.

Yes, the number of terms is 11 but we start from $$x_0$$, not from $$x_1$$, hence n=10.
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Re: In the Sequence x0, x1, x2, ..., xn, each term from x1 to xk [#permalink]

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27 Jul 2014, 06:53
Yes so the correct ans should be 11 which is not present in any of the options.
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Re: In the Sequence x0, x1, x2, ..., xn, each term from x1 to xk [#permalink]

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27 Jul 2014, 09:28
1
sri30kanth wrote:
Yes so the correct ans should be 11 which is not present in any of the options.

Еhe number of terms is 11 but we start from $$x_0$$, not from $$x_1$$, hence n=10.
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Re: In the Sequence x0, x1, x2, ..., xn, each term from x1 to xk [#permalink]

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28 Jul 2014, 09:27
1
Got it now. Thanks a lot Bunuel.
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In the Sequence x0, x1, x2, ..., xn, each term from x1 to xk [#permalink]

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10 Aug 2016, 19:39
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Top Contributor
1
Attached is a visual that should help.
Attachments

Screen Shot 2016-08-10 at 7.23.00 PM.png [ 89.74 KiB | Viewed 10851 times ]

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Re: In the Sequence x0, x1, x2, ..., xn, each term from x1 to xk [#permalink]

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02 Apr 2017, 09:51
Bunuel wrote:
kotela wrote:
In the sequence $$x_0, \ x_1, \ x_2, \ ... \ x_n$$, each term from $$x_1$$ to $$x_k$$ is 3 greater than the previous term, and each term from $$x_{k+1}$$ to $$x_n$$ is 3 less than the previous term, where $$n$$ and $$k$$ are positive integers and $$k<n$$. If $$x_0=x_n=0$$ and if $$x_k=15$$, what is the value of $$n$$?

A.5
B. 6
C. 9
D. 10
E. 15

How can i approach these kind of problems???

Probably the easiest way will be to write down all the terms in the sequence from $$x_0=0$$ to $$x_n=0$$. Note that each term from from $$x_0=0$$ to $$x_k=15$$ is 3 greater than the previous and each term from $$x_{k+1}$$ to $$x_n$$ is 3 less than the previous term:

So we'll have: $$x_0=0$$, 3, 6, 9, 12, $$x_k=15$$, 12, 9, 6, 3, $$x_n=0$$. So we have 11 terms from $$x_0$$ to $$x_n$$ thus $$n=10$$.

Hope it helps.

Bunuel: if each term from $$x_{k+1}$$ to $$x_n$$ is 3 less than the previous term and if we have k=15, why don't we start at $$x_{15+1}$$ = $$x_{16}$$? This would then change the numbers in the sequence to $$x_k=16$$ = 13, 10, 7, 4, 1 ???

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Joined: 02 Sep 2009
Posts: 46264
Re: In the Sequence x0, x1, x2, ..., xn, each term from x1 to xk [#permalink]

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19 Apr 2017, 08:02
guenthermat wrote:
Bunuel wrote:
kotela wrote:
In the sequence $$x_0, \ x_1, \ x_2, \ ... \ x_n$$, each term from $$x_1$$ to $$x_k$$ is 3 greater than the previous term, and each term from $$x_{k+1}$$ to $$x_n$$ is 3 less than the previous term, where $$n$$ and $$k$$ are positive integers and $$k<n$$. If $$x_0=x_n=0$$ and if $$x_k=15$$, what is the value of $$n$$?

A.5
B. 6
C. 9
D. 10
E. 15

How can i approach these kind of problems???

Probably the easiest way will be to write down all the terms in the sequence from $$x_0=0$$ to $$x_n=0$$. Note that each term from from $$x_0=0$$ to $$x_k=15$$ is 3 greater than the previous and each term from $$x_{k+1}$$ to $$x_n$$ is 3 less than the previous term:

So we'll have: $$x_0=0$$, 3, 6, 9, 12, $$x_k=15$$, 12, 9, 6, 3, $$x_n=0$$. So we have 11 terms from $$x_0$$ to $$x_n$$ thus $$n=10$$.

Hope it helps.

Bunuel: if each term from $$x_{k+1}$$ to $$x_n$$ is 3 less than the previous term and if we have k=15, why don't we start at $$x_{15+1}$$ = $$x_{16}$$? This would then change the numbers in the sequence to $$x_k=16$$ = 13, 10, 7, 4, 1 ???

How did you get that k=15? We are given that $$x_k=15$$, not k = 15. Also, the fact that $$x_k=15$$ does not mean that $$x_{k+1}=16$$. We are told that each term from $$x_{k+1}$$ to $$x_n$$ is 3 less than the previous term. Thus $$x_{k+1}$$ is 3 less than the previous term which is $$x_k=15$$, so $$x_{k+1}=12$$
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In the Sequence x0, x1, x2, ..., xn, each term from x1 to xk [#permalink]

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21 Apr 2017, 11:35
Bunuel wrote:

How did you get that k=15? We are given that $$x_k=15$$, not k = 15. Also, the fact that $$x_k=15$$ does not mean that $$x_{k+1}=16$$. We are told that each term from $$x_{k+1}$$ to $$x_n$$ is 3 less than the previous term. Thus $$x_{k+1}$$ is 3 less than the previous term which is $$x_k=15$$, so $$x_{k+1}=12$$

But if we are told that (a) $$x_k=15$$ and that (b) each term from $$x_{k+1}$$ to $$x_n$$ is 3 less, then the term after $$x_k=15$$ – so $$x_{k+1}$$ – will be the starting term for this reduction of 3, won't it? But if you say that the sequence is 12, $$x_k=15$$, 12, then you already start reducing by 3 as of $$x_k=15$$ which is not $$x_{k+1}$$. Do you understand my issue?
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Posts: 46264
Re: In the Sequence x0, x1, x2, ..., xn, each term from x1 to xk [#permalink]

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21 Apr 2017, 11:49
guenthermat wrote:
Bunuel wrote:

How did you get that k=15? We are given that $$x_k=15$$, not k = 15. Also, the fact that $$x_k=15$$ does not mean that $$x_{k+1}=16$$. We are told that each term from $$x_{k+1}$$ to $$x_n$$ is 3 less than the previous term. Thus $$x_{k+1}$$ is 3 less than the previous term which is $$x_k=15$$, so $$x_{k+1}=12$$

But if we are told that (a) $$x_k=15$$ and that (b) each term from $$x_{k+1}$$ to $$x_n$$ is 3 less, then the term after $$x_k=15$$ – so $$x_{k+1}$$ – will be the starting term for this reduction of 3, won't it? But if you say that the sequence is 12, $$x_k=15$$, 12, then you already start reducing by 3 as of $$x_k=15$$ which is not $$x_{k+1}$$. Do you understand my issue?

Each term from $$x_{k+1}$$ is 3 less than the previous term. So, $$x_{k+1}$$ is the first term which is 3 less than the previous term.
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Re: In the Sequence x0, x1, x2, ..., xn, each term from x1 to xk [#permalink]

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07 Oct 2017, 08:40
mydreammba wrote:
In the sequence $$x_0, \ x_1, \ x_2, \ ... \ x_n$$, each term from $$x_1$$ to $$x_k$$ is 3 greater than the previous term, and each term from $$x_{k+1}$$ to $$x_n$$ is 3 less than the previous term, where $$n$$ and $$k$$ are positive integers and $$k<n$$. If $$x_0=x_n=0$$ and if $$x_k=15$$, what is the value of $$n$$?

A. 5
B. 6
C. 9
D. 10
E. 15

How can i approach these kind of problems???

Working with the givens, X0 is your starting point. When you see this kind of sequence problem, it is best to just write the numbers out as if it were on a number line - helps with organization.

N is just a variable which represents the integers place in line. N is not related to the value of the sequencing digits. If it helps, personify math, and imagine these digits are waiting in line, and N is their ticket number.

X0, X1, X2, X3, X4, Xk (or X5), X6, X7, X8, X9, X10(Xn)
------------------------------------------
0, 3, 6 , 9, 12, 15 12 9 6 3 0

So the value of Xn is 0; but the question asks for the value of N alone, meaning its place in line.

Therefore, excluding X0, because 0 is not a value, we can conclude that the value for N is 10.

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Re: In the Sequence x0, x1, x2, ..., xn, each term from x1 to xk [#permalink]

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27 Mar 2018, 12:49
Bunuel wrote:
SOLUTION

In the sequence $$x_0, \ x_1, \ x_2, \ ... \ x_n$$, each term from $$x_1$$ to $$x_k$$ is 3 greater than the previous term, and each term from $$x_{k+1}$$ to $$x_n$$ is 3 less than the previous term, where $$n$$ and $$k$$ are positive integers and $$k<n$$. If $$x_0=x_n=0$$ and if $$x_k=15$$, what is the value of $$n$$?

(A) 5
(B) 6
(C) 9
(D) 10
(E) 15

Probably the easiest way will be to write down all the terms in the sequence from $$x_0=0$$ to $$x_n=0$$. Note that each term from from $$x_0=0$$ to $$x_k=15$$ is 3 greater than the previous and each term from $$x_{k+1}$$ to $$x_n$$ is 3 less than the previous term:

So we'll have: $$x_0=0$$, 3, 6, 9, 12, $$x_k=15$$, 12, 9, 6, 3, $$x_n=0$$. So we have 11 terms from $$x_0$$ to $$x_n$$ thus $$n=10$$.

if $$x_n=0$$ and we are asked to find the value of the value of $$n$$ ?

and there are total 11 terms, and $$x_n=0$$ is last term .... why are we saying that $$x_n = x_10$$

are we asked to find the last value of n

why are we counting 10 terms only , ok we count from zero ? so ? if i count from zero there are 11 terms ... whats point to think is it 10 ? and the tenth term is 3 by the way right ?

totally confused by the question so many questions becaus of only one question.... i got into the habit of mutliplying questions
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Re: In the Sequence x0, x1, x2, ..., xn, each term from x1 to xk [#permalink]

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27 Mar 2018, 13:55
1
dave13 wrote:
Bunuel wrote:
SOLUTION

In the sequence $$x_0, \ x_1, \ x_2, \ ... \ x_n$$, each term from $$x_1$$ to $$x_k$$ is 3 greater than the previous term, and each term from $$x_{k+1}$$ to $$x_n$$ is 3 less than the previous term, where $$n$$ and $$k$$ are positive integers and $$k<n$$. If $$x_0=x_n=0$$ and if $$x_k=15$$, what is the value of $$n$$?

(A) 5
(B) 6
(C) 9
(D) 10
(E) 15

Probably the easiest way will be to write down all the terms in the sequence from $$x_0=0$$ to $$x_n=0$$. Note that each term from from $$x_0=0$$ to $$x_k=15$$ is 3 greater than the previous and each term from $$x_{k+1}$$ to $$x_n$$ is 3 less than the previous term:

So we'll have: $$x_0=0$$, 3, 6, 9, 12, $$x_k=15$$, 12, 9, 6, 3, $$x_n=0$$. So we have 11 terms from $$x_0$$ to $$x_n$$ thus $$n=10$$.

if $$x_n=0$$ and we are asked to find the value of the value of $$n$$ ?

and there are total 11 terms, and $$x_n=0$$ is last term .... why are we saying that $$x_n = x_10$$

are we asked to find the last value of n

why are we counting 10 terms only , ok we count from zero ? so ? if i count from zero there are 11 terms ... whats point to think is it 10 ? and the tenth term is 3 by the way right ?

totally confused by the question so many questions becaus of only one question.... i got into the habit of mutliplying questions

Hi dave13

Writing down the terms helps(Here, $$x_k$$ is nothing but $$x_5$$)

$$x_0$$---$$x_1$$---$$x_2$$---$$x_3$$---$$x_4$$---$$x_5$$---$$x_6$$---$$x_7$$---$$x_8$$---$$x_9$$---$$x_{10}$$
0------3-----6-----9-----12----15----12-----9-----6-----3------0

Hope this helps you!
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Re: In the Sequence x0, x1, x2, ..., xn, each term from x1 to xk   [#permalink] 27 Mar 2018, 13:55
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