Question

3 1/2, 3 5/6, 4 2/12, ………………, 4 5/6

What is the missing term?
What rule can you create for this pattern?

Answer 1

`4(1)/(2)`

Explanation:

The sequence is
`3(1)/(2), 3(5)/(6), 4(2)/(12), .... , 4(5)/(6)`.

So, we have to find the missing term.

The sequence can be written in improper fraction as
`(7)/(2), (23)/(6), (25)/(6), ... , (29)/(6)`.

Therefore, the sequence is in A.P. as the consecutive numbers in the sequence are increasing by
`(1)/(3)`.

As,
`((23)/(6) - (7)/(2)) = (1)/(3) = ((25)/(6) - (23)/(6))`.

Therefore, the missing number is
`((25)/(6) + (1)/(3)) = (27)/(6) = (9)/(2) = 4(1)/(2)`. (Answer)