Question

What is the next fraction in this sequence? Simplify your answer. 2/7, 5/14, 3/7, 1/2, ......

Answer 1

We are given the following sequence

`(2)/(7),(5)/(14),(3)/(7),(1)/(2),\ldots`

Let us check if there is a common difference between the consecutive terms

`\begin{gathered} (5)/(14)-(2)/(7)=(5-2(2))/(14)=(5-4)/(14)=(1)/(14) \\ (3)/(7)-(5)/(14)=(2(3)-5)/(14)=(6-5)/(14)=(1)/(14) \\ (1)/(2)-(3)/(7)=(7(1)-2(3))/(14)=(7-6)/(14)=(1)/(14) \end{gathered}`

As you can see, there is a common difference between the terms that is 1/14

If we add 1/14 to the last term of the sequence (1/2) then we would get the next fraction in the sequence.