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# the sequence x1,x2 ... xn is such that x1=5, x2=-5, x3=0, x4=-2

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Intern
Joined: 17 Jan 2017
Posts: 46
the sequence x1,x2 ... xn is such that x1=5, x2=-5, x3=0, x4=-2 [#permalink]

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07 Apr 2018, 04:12
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65% (hard)

Question Stats:

40% (01:23) correct 60% (02:32) wrong based on 25 sessions

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The sequence $$x_1$$,$$x_2$$ ... $$x_n$$ is such that $$x_1$$ = 5, $$x_2$$ = -5, $$x_3$$ = 0, $$x_4$$ = -2, $$x_5$$ = 4 and $$x_n$$= $$x_{n-5}$$. If the sum of the first P terms as well as the sum of the first P-3 terms is 18, P= ?

A. 39
B. 42
C. 45
D. 48
E. 51

Source: ExpertsGlobal
[Reveal] Spoiler: OA
Math Expert
Joined: 02 Aug 2009
Posts: 5777
Re: the sequence x1,x2 ... xn is such that x1=5, x2=-5, x3=0, x4=-2 [#permalink]

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07 Apr 2018, 18:51
benejo wrote:
The sequence $$x_1$$,$$x_2$$ ... $$x_n$$ is such that $$x_1$$ = 5, $$x_2$$ = -5, $$x_3$$ = 0, $$x_4$$ = -2, $$x_5$$ = 4 and $$x_n$$= $$x_{n-5}$$. If the sum of the first P terms as well as the sum of the first P-3 terms is 18, P= ?

A. 39
B. 42
C. 45
D. 48
E. 51

Source: ExpertsGlobal

The first 5 terms are being repeated, so let's see their SUM..
5+(-5)+0+(-2)+4=2...
So 18 will be 2*9, that is it will be sum of 9 such sets, each containing 5 numbers..
So number =5*9=45..
But we are given both P and P-3 have same sum..
If we go down by 3 terms, it will change the sum by 4+(-2)+0=2, so sum will be 18-2=16..

Therefore add the next three terms = 5+(-5)+0=0..
So these will not effect the SUM and sum will remain 18..
So P-3=45....P=45+3=48

D
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Re: the sequence x1,x2 ... xn is such that x1=5, x2=-5, x3=0, x4=-2   [#permalink] 07 Apr 2018, 18:51
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# the sequence x1,x2 ... xn is such that x1=5, x2=-5, x3=0, x4=-2

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