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The sequence of the 50 numbers a_1, a_2 , ..., a_50 is defined as foll

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Bunuel
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The sequence of the 50 numbers a_1, a_2 , ..., a_50 is defined as foll [#permalink] New post   07 Mar 2023, 10:23
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The sequence of the 50 numbers \(a_1\), \(a_2\), ..., \(a_{50}\) is defined as follows, where n is an integer between 1 and 50, inclusive.

\(a_n=\frac{n+1}{n}-1\) if n is odd

\(a_n = -a_{n-1}\) if n is even

What is range of the first 15 terms of the sequence?

A) \(\frac{2}{3}\)

B) \(1\)

C) \(\frac{4}{3}\)

D) \(2\)

E) \(\frac{8}{3}\)
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prachisaraf
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Re: The sequence of the 50 numbers a_1, a_2 , ..., a_50 is defined as foll [#permalink] New post   11 Mar 2023, 11:06
Could someone post the solution explanation? Thanks!
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Re: The sequence of the 50 numbers a_1, a_2 , ..., a_50 is defined as foll [#permalink] New post   12 Mar 2023, 18:38
I am not sure what is the meaning of the range?
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Re: The sequence of the 50 numbers a_1, a_2 , ..., a_50 is defined as foll [#permalink] New post   13 Mar 2023, 03:12
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Bunuel wrote:
The sequence of the 50 numbers \(a_1\), \(a_2\), ..., \(a_{50}\) is defined as follows, where n is an integer between 1 and 50, inclusive.

\(a_n=\frac{n+1}{n}-1\) if n is odd

\(a_n = -a_{n-1}\) if n is even

What is range of the first 15 terms of the sequence?

A) \(\frac{2}{3}\)

B) \(1\)

C) \(\frac{4}{3}\)

D) \(2\)

E) \(\frac{8}{3}\)


\(a_n=\frac{n+1}{n}-1=\frac{n+1-n}{n}=\frac{1}{n}\) if n is odd

\(a_n = -a_{n-1}\) if n is even

So, basically odd terms equal to 1/n and even terms equal to -(previous term). Hence, the sequence goes as follow:

1, -1, 1/3, -1/3, 1/5, -1/5, ..., 1/13, -1/13, 1/15, ...

The range of numbers is the difference between the largest and smallest of these numbers. The largest number is 1, and the smallest number is -1. Therefore, the range of these 15 numbers is 1 - (-1) = 2.

Answer: D.
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Re: The sequence of the 50 numbers a_1, a_2 , ..., a_50 is defined as foll [#permalink]
13 Mar 2023, 03:12
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