What is the missing number ? 1/> 1/> 1/> 2/> 1/> 5/> 2/> ? > 5/6

The first four terms of the sequence are 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 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 increased by one. So the value of each next term increase by 1/6

Therefore the sequence is in arithmetic progression (or AP) with common difference of the sequence is1/6, and the starting term is 1/6. Therefore, the general 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 giving 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 answer is 0.3175 hope that you ^w^

also you might actually want to put this picture up if you want people to solve it luckily i remember this question

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step-by-step explanation: