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

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Math Expert
Joined: 02 Sep 2009
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Does the sequence a1, a2, a3, ..., an, ... contain an infinite number  [#permalink]

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19 Nov 2019, 02:00
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Difficulty:

75% (hard)

Question Stats:

37% (01:33) correct 63% (02:00) wrong based on 43 sessions

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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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19 Nov 2019, 07:41
1
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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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.

1: Clearly says, No.

hence A is sufficient.

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

Not sufficient.

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

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

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07 Dec 2019, 06:31
1
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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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?
Intern
Joined: 26 Jun 2017
Posts: 18
Re: Does the sequence a1, a2, a3, ..., an, ... contain an infinite number  [#permalink]

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09 Dec 2019, 11:43
1
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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