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# A sequence An is there such that An=(An-1)-(An-2) where n are integers

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A sequence An is there such that An=(An-1)-(An-2) where n are integers  [#permalink]

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17 Feb 2017, 23:57
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Difficulty:

75% (hard)

Question Stats:

51% (02:06) correct 49% (01:34) wrong based on 121 sessions

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A sequence $$A_n$$ is there such that $$A_{n}=A_{n-1}-A_{n-2}$$ where $$n$$ are integers greater than $$2$$. What is the value of $$A_5$$?

(1) $$A_{4} - A_{3}=3$$
(2) $$A_{14}=1$$

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Re: A sequence An is there such that An=(An-1)-(An-2) where n are integers  [#permalink]

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18 Feb 2017, 01:31
1
ziyuenlau wrote:
A sequence $$A_n$$ is there such that $$A_{n}=A_{n-1}-A_{n-2}$$ where $$n$$ are integers greater than $$2$$. What is the value of $$A_5$$?

(1) $$A_{4} - A_{3}=3$$
(2) $$A_{14}=1$$

Hi

Nice question.

(1) This is fairy straightforward. $$A_5 = A_4 - A_3 = 3$$ Sufficient

(2) This one is tricky.

In fact we have only two variables to operate - $$A_1$$ and $$A_2$$.

$$A_3 = A_2 - A_1$$

$$A_4 = A_3 - A_2 = - A_1$$

$$A_5 = A_4 - A_3 = - A_2$$

$$A_6 = A_5 - A_4 = - A_3$$

$$A_7 = A_6 - A_5 = A_1$$

$$A_8 = A_7 - A_6 = A_2$$

$$A_9 = A_8 - A_7 = A_3$$

We could have stopped at $$A_7$$ but $$A_9$$ gives better picture of the full cycle. As we can see, we have a cycle of 6, after $$A_6$$ which the pattern repeats.

$$A_1, A_2, A_3, - A_1, - A_2, - A_3, A_1 ...$$

$$A_{14}$$ give remainder $$2$$ upon division by $$6$$, that is $$A_{14} = A_2 = 1$$

$$A_5 = - A_2 = - 1$$ Sufficient

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Re: A sequence An is there such that An=(An-1)-(An-2) where n are integers  [#permalink]

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04 May 2017, 12:27
1
ziyuen wrote:
A sequence $$A_n$$ is there such that $$A_{n}=A_{n-1}-A_{n-2}$$ where $$n$$ are integers greater than $$2$$. What is the value of $$A_5$$?

(1) $$A_{4} - A_{3}=3$$
(2) $$A_{14}=1$$

Hmm.. Even tough we can get an answer from each statement, I would say that this is not a good quality question. In GMAT DS, Statement 1 and Statement 2 give the exact same answer rather than 2 different ones like in this question.

Anyways,

From Statement 1, $$A_5$$ = 3

From Statement 2, $$A_5$$ = -1

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Re: A sequence An is there such that An=(An-1)-(An-2) where n are integers  [#permalink]

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12 Nov 2017, 10:08

But two statements contradicting giving two diff values for A5
Re: A sequence An is there such that An=(An-1)-(An-2) where n are integers &nbs [#permalink] 12 Nov 2017, 10:08
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