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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, 01:20
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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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Kudos [?]: 89906 [2] , given: 10382

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

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05 Mar 2014, 01:20
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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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Kudos [?]: 1830 [0], given: 193

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

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05 Mar 2014, 19:25
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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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Math Expert
Joined: 02 Sep 2009
Posts: 35865
Followers: 6837

Kudos [?]: 89906 [0], given: 10382

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

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08 Mar 2014, 11:40
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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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26 Jul 2014, 21:17
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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Kudos [?]: 89906 [1] , given: 10382

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

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27 Jul 2014, 02:25
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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, 05:53
Yes so the correct ans should be 11 which is not present in any of the options.
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Kudos [?]: 89906 [1] , given: 10382

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

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27 Jul 2014, 08:28
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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, 08:27
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Got it now. Thanks a lot Bunuel.
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Re: In the Sequence x0, x1, x2, ..., xn, each term from x1 to xk [#permalink]

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28 Sep 2015, 16:34
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Re: In the Sequence x0, x1, x2, ..., xn, each term from x1 to xk [#permalink]

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13 Nov 2016, 16:07
Hello from the GMAT Club BumpBot!

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Re: In the Sequence x0, x1, x2, ..., xn, each term from x1 to xk   [#permalink] 13 Nov 2016, 16:07
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