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Question

Four fractions are arranged from the smallest to the largest, 1/3, P, Q, 1/2. The difference between any two adjacent fractions is the same. Find the two missing fractions P and Q.

Answer

If u is the difference between 1/3 and the next term,

1/3 + 3u = 1/2

3u = 1/2 – 1/3 = (3-2)/6 = 1/6

u = 1/18

So P = 1/3 + 1/18 = 7/18

and Q = 7/18 + 1/18 = 8/18

Check:  the four terms look like, 6/18 ,7/18 , 8/18 , 9/18. 

6/18 = 1/3

and 9/18 = 1/2

 

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