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For the infinite sequence of numbers a1, a2, a3, ..., an, ..., for all [#permalink]

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16 Jul 2016, 08:08

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For the infinite sequence of numbers \(a_1\), \(a_2\), \(a_3\), ..., \(a_n\), ..., for all n > 1, \(a_n\) = \(a_{n−1}\) + 4 if n is odd and \(a_n\) = \(a_{n−1}\) - 1 if n is even. What is the value of \(a_1\) if \(a_{34}\) = 68?

Re: For the infinite sequence of numbers a1, a2, a3, ..., an, ..., for all [#permalink]

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16 Jul 2016, 10:03

EBITDA wrote:

For the infinite sequence of numbers \(a_1\), \(a_2\), \(a_3\), ..., \(a_n\), ..., for all n > 1, \(a_n\) = \(a_{n−1}\) + 4 if n is odd and \(a_n\) = \(a_{n−1}\) - 1 if n is even. What is the value of \(a_1\) if \(a_{34}\) = 68?

A) 10 B) 11 C) 12 D) 13 E) 21

\(a_{34}\) = 68 = \(a_{33}\) - 1 = \(a_{32}\) - 1 +4 ... and so on

So observing the trend,

\(a_{34}\) = \(a_{1}\) +(32/2) * 4 - (34/2) * (-1) [32/2 to get all the even n (from 32 to 2) and 34/2 to get all the odd n (from 33 to 1) including 33 and 1]

Re: For the infinite sequence of numbers a1, a2, a3, ..., an, ..., for all [#permalink]

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17 Jul 2016, 02:47

14101992 wrote:

EBITDA wrote:

For the infinite sequence of numbers \(a_1\), \(a_2\), \(a_3\), ..., \(a_n\), ..., for all n > 1, \(a_n\) = \(a_{n−1}\) + 4 if n is odd and \(a_n\) = \(a_{n−1}\) - 1 if n is even. What is the value of \(a_1\) if \(a_{34}\) = 68?

A) 10 B) 11 C) 12 D) 13 E) 21

\(a_{34}\) = 68 = \(a_{33}\) - 1 = \(a_{32}\) - 1 +4 ... and so on

So observing the trend,

\(a_{34}\) = \(a_{1}\) +(32/2) * 4 - (34/2) * (-1) [32/2 to get all the even n (from 32 to 2) and 34/2 to get all the odd n (from 33 to 1) including 33 and 1]

\(a_{1}\) = 68-64+17 = 21

Hence, answer will be E.

-------------------------------------

P.S. Don't forget to give Kudos

Thank you for your explanation.

Nonetheless, I think that the bold part of your explanation should rather be:

32/2 to get all the odd n (from 33 to 1, including 33 but excluding 1, as you are already including \(a_{1}\) in your formula) and 34/2 to get all the even n (from 34 to 2, including both).

Re: For the infinite sequence of numbers a1, a2, a3, ..., an, ..., for all [#permalink]

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07 Oct 2016, 06:36

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EBITDA wrote:

For the infinite sequence of numbers \(a_1\), \(a_2\), \(a_3\), ..., \(a_n\), ..., for all n > 1, \(a_n\) = \(a_{n−1}\) + 4 if n is odd and \(a_n\) = \(a_{n−1}\) - 1 if n is even. What is the value of \(a_1\) if \(a_{34}\) = 68?

A) 10 B) 11 C) 12 D) 13 E) 21

we have 34 consecutive numbers... 17 are even 17 are odd.. since we need to find a1 -> then we must disregard first odd number. since odd means +4, then multiply 16 by 4. we get 64. since we have 17 even numbers, we subtract 17. so... a1+64-17=68 a1+47=68 a1=21.