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

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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**

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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