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Each term, starting from the third term, of a sequence [#permalink]

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17 Jul 2017, 22:26

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Each term, starting from the third term, of a sequence, which has 98 terms, is the sum of the two preceding terms. If the first two terms of the sequence are odd numbers, then what is the ratio of the number of odd valued terms to that of even valued terms?

Each term, starting from the third term, of a sequence [#permalink]

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17 Jul 2017, 23:09

TimeTraveller wrote:

Each term, starting from the third term, of a sequence, which has 98 terms, is the sum of the two preceding terms. If the first two terms of the sequence are odd numbers, then what is the ratio of the number of odd valued terms to that of even valued terms?

If first two terms are Odd, third would be Even, 4th would be E + O = Odd, so sequence becomes.

O O E O

fifth would again be Odd because E + O = O

O O E O O

Now 6th term would be Even because 4th and 5th are both odd and this sequence repeats.

O O E O O E O O E

If this sequence goes on 33 times, terms would be 99 and last term would be even but we have trimmed the last Even term out.

so we have 33 x 2 odd and 32 Even terms.

66:32 = 33:16
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Each term, starting from the third term, of a sequence, which has 98 terms, is the sum of the two preceding terms. If the first two terms of the sequence are odd numbers, then what is the ratio of the number of odd valued terms to that of even valued terms?

Odd + Odd = Even So third term is even. We have Odd, Odd, Even

Odd + Even = Odd So fourth term is Odd. We have Odd, Odd, Even, Odd

Even + Odd = Odd So fifth term is Odd. We have Odd, Odd, Even, Odd, Odd

Now, we again have 2 odd terms to the pattern will continue.

Odd, Odd, Even, Odd, Odd, Even, Odd, Odd, Even... and so on In every 3 terms, 2 are Odd and 1 is Even. So in 99 terms, 66 would be Odd and 33 would be Even,the last one being Even. If we have only 98 terms, we would have 66 Odd and 32 Even.

Each term, starting from the third term, of a sequence, which has 98 terms, is the sum of the two preceding terms. If the first two terms of the sequence are odd numbers, then what is the ratio of the number of odd valued terms to that of even valued terms?

We see that each term that is a multiple of 3 is even and all other terms are odd.

From 1 to 98, there are (96 - 3)/3 + 1 = 32 multiples of 3, and thus there are 32 even terms. So, there are 98 - 32 = 66 odd terms. So, the ratio of odd-valued terms to even-valued terms is 66/32 = 33/16.

Answer: B
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Re: Each term, starting from the third term, of a sequence [#permalink]

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20 Jul 2017, 21:15

TimeTraveller wrote:

Each term, starting from the third term, of a sequence, which has 98 terms, is the sum of the two preceding terms. If the first two terms of the sequence are odd numbers, then what is the ratio of the number of odd valued terms to that of even valued terms?

Re: Each term, starting from the third term, of a sequence [#permalink]

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08 Sep 2017, 12:13

VeritasPrepKarishma wrote:

TimeTraveller wrote:

Each term, starting from the third term, of a sequence, which has 98 terms, is the sum of the two preceding terms. If the first two terms of the sequence are odd numbers, then what is the ratio of the number of odd valued terms to that of even valued terms?

Odd + Odd = Even So third term is even. We have Odd, Odd, Even

Odd + Even = Odd So fourth term is Odd. We have Odd, Odd, Even, Odd

Even + Odd = Odd So fifth term is Odd. We have Odd, Odd, Even, Odd, Odd

Now, we again have 2 odd terms to the pattern will continue.

Odd, Odd, Even, Odd, Odd, Even, Odd, Odd, Even... and so on In every 3 terms, 2 are Odd and 1 is Even. So in 99 terms, 66 would be Odd and 33 would be Even,the last one being Even. If we have only 98 terms, we would have 66 Odd and 32 Even.