Question

15. Predict the next three numbers in each pattern. a) 7 1 3 -13 2' 8' 4' 8 -- -- 2 1 1 1 1, .. b) 11 3' 3' 3' 6' 12'

Answer 1

Problem

Solution

Part a

-1 1/2 , -7/8 , -1/4 , 3/8, 1,....

We can rewrite the sequence like this:

-3/2, -7/8, -1/4, 3/8, 1,...

For this case the difference between consecutive terms is:

-7/8 -( -3/2) = -7/8 +3/2= 5/8

And we can find the next 3 terms like this:

1+ 5/8= 13/8

13/8 + 5/8 = 18/8

18/8 + 5/8 = 23/8

Answer: 13/8, 18/8, 23/8

Part b

1 1/3 , -2/3, 1/3, -1/6, 1/12

We can rewrite the sequence like this:

4/3, -2/3, 1/3, -1/6, 1/12,

We can see that each term is divided by 2 and we can do this:

1/12 /(-2)= -1/24

1/24 /(2)= 1/48

1/48 /(-2) = -1/96

The answer for part b is:

-1/24, 1/48, -1/96