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What is the next two answers in this sequence: 1/6, 1/3, 1/2, 2/3?

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alvad9 | eNotes Newbie

Posted August 10, 2009 at 1:39 PM via web

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What is the next two answers in this sequence: 1/6, 1/3, 1/2, 2/3?

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neela | High School Teacher | Valedictorian

Posted August 10, 2009 at 4:59 PM (Answer #1)

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The first 4 terms of the sequence  is given. Let us examine what type of sequence is it  and find the general term of the sequence by which we can generate any term of the sequence.

Let us find the the Least Common Multiple( or LCM)  of denominators of the first 4 terms given:

The denominators of the 4 terms are 6,3,2,3 and obviously 6 is the LCM. Now let us convert the terms into equivalent fractions with denominators  as 6,the LCM.

Then the 1st term of sequence is 1/6 = 1/6

2nd term of the sequence =1/3= 2/6

3rd term=1/2=3/6

4th term=2/3=4/6

Obviously the numerator is increasing by one. So the value of each next term increase by 1/6

Therefore the seqence  is in arithmetic progression (or AP) with common  difference of the sequence is1/6 , and the starting term is 1/6. Therefore, the genaral nth term of the sequence  = starting term+(n-1)*common difference= 1/6+(n-1)(1/6)=n/6. So any  term of the sequence  {n/6} can easily be generated by givin n a suitable value.

The next term is 5th and 6th are got by putting n=5 and n=6

So the  5th term = 5/6

The 6th term = 6/6=1

 

 

 

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krishna-agrawala | College Teacher | Valedictorian

Posted August 10, 2009 at 2:01 PM (Answer #2)

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The given sequence is:

1/6, 1/3, 1/2, 2/3, ...

This can also be represented as:

1/6, 2/6, 3/6, 4/6, ...

Therefore the next two terms in the sequence are 5/6 and 6/6.

Thus the extended sequence containing six terms is

1/6, 1/3, 1/2, 2/3, 5/6, 1, ...

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