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A sequence of terms a1, a2 ,a3, ..., a(m-1), am, is given by [#permalink]
06 Apr 2013, 04:08

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Difficulty:

65% (hard)

Question Stats:

62% (02:23) correct
38% (01:39) wrong based on 97 sessions

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]
06 Apr 2013, 04:29

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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]
06 Sep 2013, 11:12

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]
19 Nov 2013, 22:58

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]
20 Nov 2013, 00:32

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. _________________