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A sequence of terms a1, a2 ,a3, ..., a(m-1), am, is given by [#permalink]

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06 Apr 2013, 05:08

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Difficulty:

65% (hard)

Question Stats:

64% (02:27) correct
36% (01:40) wrong based on 162 sessions

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A sequence of non-zero terms \(a_1\), \(a_2\), \(a_3\), ..., \(a_{m-1}\), \(a_m\), is given by \(a_k=(a_{k-1})^2(a_{k-2})\) for every k>2. If m=12, then how many terms in the given sequence are positive?

(1) \(a_3\) is positive (2) \(a_4\) is positive

My apologies . I could not find a way to type the sequence here , so I am attaching the DS question .

Re: A sequence of terms a1, a2 ,a3, ..., a(m-1), am, is given by [#permalink]

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06 Apr 2013, 05:29

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Expert's post

A sequence of non-zero terms \(a_1\), \(a_2\), \(a_3\), ..., \(a_{m-1}\), \(a_m\), is given by \(a_k=(a_{k-1})^2(a_{k-2})\) for every k>2. If m=12, then how many terms in the given sequence are positive?

From above: \(a_3=(a_2)^2*a_1\); \(a_4=(a_3)^2*a_2\); ...

(1) \(a_3\) is positive --> \(a_3=(a_2)^2*a_1=positive\) --> \(a_1=positive\). Now, if \(a_1=a_2=1\), then ALL 12 terms in the sequence will be positive but if \(a_1=1\), and \(a_2=-1\) (\(a_3=(a_2)^2*a_1=(-1)^2*1=1=positive\)), then not all the terms in the sequence will be positive. Not sufficient.

(2) \(a_4\) is positive --> \(a_4=(a_3)^2*a_2=positive\) --> \(a_2=positive\). The same here: if \(a_1=a_2=1\), then ALL 12 terms in the sequence will be positive but if \(a_1=-1\), and \(a_2=1\) (\(a_3=(a_2)^2*a_1=(1)^2*(-1)=-1\) and \(a_4=(a_3)^2*a_2=(-1)^2*1=1=positive\)), then not all the terms in the sequence will be positive. Not sufficient.

(1)+(2) From above we have that \(a_1=positive\) and \(a_2=positive\). Therefore, all 12 terms of the sequence are positive. Sufficient.

Re: A sequence of terms a1, a2 ,a3, ..., a(m-1), am, is given by [#permalink]

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07 Apr 2013, 22:33

Expert's post

marcovg4 wrote:

Then.. The information for "every k>2" is irrelevant right

Posted from my mobile device

"A sequence ... is given by \(a_k=(a_{k-1})^2(a_{k-2})\) for every k>2" means that the given formula applies for the terms starting \(a_3\). _________________

Re: A sequence of terms a1, a2 ,a3, ..., a(m-1), am, is given by [#permalink]

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06 Sep 2013, 12:12

Bunuel wrote:

A sequence of non-zero terms \(a_1\), \(a_2\), \(a_3\), ..., \(a_{m-1}\), \(a_m\), is given by \(a_k=(a_{k-1})^2(a_{k-2})\) for every k>2. If m=12, then how many terms in the given sequence are positive?

From above: \(a_3=(a_2)^2*a_1\); \(a_4=(a_3)^2*a_2\); ...

(1) \(a_3\) is positive --> \(a_3=(a_2)^2*a_1=positive\) --> \(a_1=positive\). Now, if \(a_1=a_2=1\), then ALL 12 terms in the sequence will be positive but if \(a_1=1\), and \(a_2=-1\) (\(a_3=(a_2)^2*a_1=(-1)^2*1=1=positive\)), then not all the terms in the sequence will be positive. Not sufficient.

(2) \(a_4\) is positive --> \(a_4=(a_3)^2*a_2=positive\) --> \(a_2=positive\). The same here: if \(a_1=a_2=1\), then ALL 12 terms in the sequence will be positive but if \(a_1=-1\), and \(a_2=1\) (\(a_3=(a_2)^2*a_1=(1)^2*(-1)=-1\) and \(a_4=(a_3)^2*a_2=(-1)^2*1=1=positive\)), then not all the terms in the sequence will be positive. Not sufficient.

(1)+(2) From above we have that \(a_1=positive\) and \(a_2=positive\). Therefore, all 12 terms of the sequence are positive. Sufficient.

Answer: C.

Hope it's clear.

Although the Answer is correct..but as I see the question Posted and the question in the image are different. Considering the question in the image a1 = +ve, a2=-ve, a3=+ve, a4=-ve and so on...Therefore, there will be 6 +ve terms in the sequence...

Re: A sequence of terms a1, a2 ,a3, ..., a(m-1), am, is given by [#permalink]

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19 Nov 2013, 23:58

guerrero25 wrote:

A sequence of non-zero terms \(a_1\), \(a_2\), \(a_3\), ..., \(a_{m-1}\), \(a_m\), is given by \(a_k=(a_{k-1})^2(a_{k-2})\) for every k>2. If m=12, then how many terms in the given sequence are positive?

(1) \(a_3\) is positive (2) \(a_4\) is positive

My apologies . I could not find a way to type the sequence here , so I am attaching the DS question .

Statement 2 in the question and in the screenshot are different! is \(a_4\) positive or negative?

Re: A sequence of terms a1, a2 ,a3, ..., a(m-1), am, is given by [#permalink]

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20 Nov 2013, 01:32

Expert's post

emailmkarthik wrote:

guerrero25 wrote:

A sequence of non-zero terms \(a_1\), \(a_2\), \(a_3\), ..., \(a_{m-1}\), \(a_m\), is given by \(a_k=(a_{k-1})^2(a_{k-2})\) for every k>2. If m=12, then how many terms in the given sequence are positive?

(1) \(a_3\) is positive (2) \(a_4\) is positive

My apologies . I could not find a way to type the sequence here , so I am attaching the DS question .

Statement 2 in the question and in the screenshot are different! is \(a_4\) positive or negative?

The discussion is on the question which says that \(a_4\) is positive. _________________

Re: A sequence of terms a1, a2 ,a3, ..., a(m-1), am, is given by [#permalink]

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10 Sep 2015, 01:22

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