What is the next fraction in this sequence? Simplify your answer. 7 18 , 1 3 , 5 18 , 2 9 , ...

Answer 1

Almost all of these pattern/sequence questions have a sequence that is either.

1. Adding or Subtracting by a constant amount.
2. Multiplying or Dividing by a constant amount.

We can easily check if it is case #1 by normalizing all the denominators with a least common multiple, like so.

7/18

6/18 (1/3)

5/18

4/18 (2/9)

From here the pattern seems rather clear, no? Seems to be a clear case of subtracting by a constant. (1/18)

If you want to do this faster next time, you could also note that there is a 7/18 that decreases to 5/18 in 2 steps, where you could probably guess this result, and then you could quickly check afterwards.

Answer 2

What is the next fraction in this sequence? Simplify your answer. 7 18 , 1 3 , 5 18 , 2 9 , ...

This is simply counting down by 1/18 [ Arithmetic Sequence with d = -1/18 ]

7/18

6/18

5/18

4/18

3/18

. . .

[Reduce fractions to check this list.]