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# An infinite sequence of positive integers is called a "beta

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An infinite sequence of positive integers is called a "beta [#permalink]

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01 May 2013, 09:08
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An infinite sequence of positive integers is called a "beta Sequence" if the number of odd integers in the sequence is finite. If S is an infinite sequence of positive integers, is S a beta sequence?

(1) The first ten integers in S are even.
(2) The difference between each successive pair of terms in S is a constant
[Reveal] Spoiler: OA

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Re: An infinite sequence of positive integers is called a "beta [#permalink]

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01 May 2013, 09:16
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Expert's post
manishuol wrote:
An infinite sequence of positive integers is called a "beta Sequence" if the number of odd integers in the sequence is finite. If S is an infinite sequence of positive integers, is S a beta sequence?

(1) The first ten integers in S are even.
(2) The difference between each successive pair of terms in S is a constant

Similar question to practice:
Quote:
An infinite sequence of positive integers is called an "alpha sequence" if the number of even integers in the sequence is finite. If S is an infinite sequence of positive integers, is S an alpha sequence?

(1) The first ten integers in S are even.
(2) An infinite number of integers in S are odd.

Discussed here: an-infinite-sequence-of-positive-integers-is-called-an-101758.html

Hope it helps.
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Re: An infinite sequence of positive integers is called a "beta [#permalink]

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01 May 2013, 09:18
Bunuel wrote:
manishuol wrote:
An infinite sequence of positive integers is called a "beta Sequence" if the number of odd integers in the sequence is finite. If S is an infinite sequence of positive integers, is S a beta sequence?

(1) The first ten integers in S are even.
(2) The difference between each successive pair of terms in S is a constant

Similar question to practice:
Quote:
An infinite sequence of positive integers is called an "alpha sequence" if the number of even integers in the sequence is finite. If S is an infinite sequence of positive integers, is S an alpha sequence?

(1) The first ten integers in S are even.
(2) An infinite number of integers in S are odd.

Discussed here: an-infinite-sequence-of-positive-integers-is-called-an-101758.html

Hope it helps.

Thanks !! Bunuel .........
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Re: An infinite sequence of positive integers is called a "beta [#permalink]

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03 May 2013, 00:47
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[quote="manishuol"]An infinite sequence of positive integers is called a "beta Sequence" if the number of odd integers in the sequence is finite. If S is an infinite sequence of positive integers, is S a beta sequence?

to become a beta sequence number of odd integers in the sequence must be finite
(1) The first ten integers in S are even.

We dont know the number rest all number are odd or even....so not sufficient.

(2) The difference between each successive pair of terms in S is a constant

difference is constant ..it means this series is an AP.....but as we dont know the numbers...it can be AP Of oDD OR EVEN...so not sufficeint.

combining....we know this is an AP and plus we also know that first 10 terms are even ..it means rest all terms are also even...so we don have odd numbers....so means it is finite...
hence..C

hope it helps.

SKM
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Re: An infinite sequence of positive integers is called a "beta [#permalink]

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15 Jan 2014, 06:10
manishuol wrote:
An infinite sequence of positive integers is called a "beta Sequence" if the number of odd integers in the sequence is finite. If S is an infinite sequence of positive integers, is S a beta sequence?

(1) The first ten integers in S are even.
(2) The difference between each successive pair of terms in S is a constant

I thought that if we had an infinite sequence and in this infinite sequence we have 10 integers that are even, then the number of odds in this infinite sequence has to be finite. I don't quite get it.

Anyone thought the same way?

Cheers!
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Re: An infinite sequence of positive integers is called a "beta [#permalink]

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26 Sep 2016, 23:38
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Re: An infinite sequence of positive integers is called a "beta   [#permalink] 26 Sep 2016, 23:38
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