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

Question

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}

prachisaraf · Answer

Could someone post the solution explanation? Thanks!

Gmat7552021 · Answer

I am not sure what is the meaning of the range?

Bunuel · Answer

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

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

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