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Does the sequence a1, a2, a3, ..., an, ... contain an infinite number

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Does the sequence a1, a2, a3, ..., an, ... contain an infinite number  [#permalink]

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New post 19 Nov 2019, 02:00
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Does the sequence \(a_1\), \(a_2\), \(a_3\), ..., \(a_n\), ... contain an infinite number of terms that are divisible by 20?

(1) \(a_1 = 5\) and \(a_n = 4*5^{(n – 1)}\) for all integers \(n ≥ 2\).

(2) \(a_2 = 20\), \(a_4 = 500\), \(a_5 = 2,500\), and \(a_6 = 12,500\).


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Re: Does the sequence a1, a2, a3, ..., an, ... contain an infinite number  [#permalink]

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New post 19 Nov 2019, 07:41
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Does the sequence \(a_1\), \(a_2\), \(a_3\), ..., \(a_n\), ... contain an infinite number of terms that are divisible by 20?

(1) \(a_1 = 5\) and \(a_n = 4*5^{(n – 1)}\) for all integers \(n ≥ 2\).
\(a_1 = 5\), so it is NOT divisible by 20. Hence our answer is NO
Suff

(2) \(a_2 = 20\), \(a_4 = 500\), \(a_5 = 2,500\), and \(a_6 = 12,500\).
We do not know anything about of other terms, although the given terms are surely multiple of 20. We cannot say a definite yes or definite no..

A
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Does the sequence a1, a2, a3, ..., an, ... contain an infinite number  [#permalink]

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New post 22 Nov 2019, 09:51
Does the sequence a1, a2, a3, ..., an, ... contain an infinite number of terms that are divisible by 20?

(1) a1=5a1=5 and an=4∗5(n–1)an=4∗5(n–1) for all integers n≥2n≥2.

(2) a2=20, a4=500, a5=2,500, and a6=12,500.


Answer is A,

1: Clearly says, No.

hence A is sufficient.

2: Yes no.yes no......no idea of a1 ???a3???a4???

Not sufficient.

Answer is A
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Re: Does the sequence a1, a2, a3, ..., an, ... contain an infinite number  [#permalink]

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New post 07 Dec 2019, 04:06
chetan2u wrote:
Does the sequence \(a_1\), \(a_2\), \(a_3\), ..., \(a_n\), ... contain an infinite number of terms that are divisible by 20?

(1) \(a_1 = 5\) and \(a_n = 4*5^{(n – 1)}\) for all integers \(n ≥ 2\).
\(a_1 = 5\), so it is NOT divisible by 20. Hence our answer is NO
Suff

(2) \(a_2 = 20\), \(a_4 = 500\), \(a_5 = 2,500\), and \(a_6 = 12,500\).
We do not know anything about of other terms, although the given terms are surely multiple of 20. We cannot say a definite yes or definite no..

A


I didn't get why is the answer to first statement 'NO'?
Could you please explain?
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Re: Does the sequence a1, a2, a3, ..., an, ... contain an infinite number  [#permalink]

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New post 07 Dec 2019, 06:31
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Hey,

a1=5 and an=4∗5^(n–1)for all integers n≥2.

sequence is a1,a2,a3,-----

a1 = 5 , 5 is not divisible by 20.

rest does not matter.

hence information clearly says sufficient.
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Re: Does the sequence a1, a2, a3, ..., an, ... contain an infinite number  [#permalink]

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New post 09 Dec 2019, 11:30
please explain why the first statement isn't sufficient...it is talking about infinite number of terms ...so why bother about a single first term?
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Re: Does the sequence a1, a2, a3, ..., an, ... contain an infinite number  [#permalink]

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New post 09 Dec 2019, 11:43
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I have doubts in both the statments

1.Like Bikramjeet said when the question says infinite number of terms why are we bothering about a single term. Infinite number of terms does not not mean all terms, right ?


2. Thought we do not know about the other terms. We can still deduce what the other terms could be.

I request someone clarify my doubt.

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Re: Does the sequence a1, a2, a3, ..., an, ... contain an infinite number   [#permalink] 09 Dec 2019, 11:43
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