predict the next three numbers in the pattern.16,4,1,1/4,1/16

Question

predict the next three numbers in the pattern.16,4,1,1/4,1/16

Answer 1

Arturo:

 

This problem requires that you are able to spot a pattern in the numbers given.  What relationship do you see?  For example, if the pattern was 5,10,15, 20 and you were asked to predict the next three numbers, you would observe that each number in the pattern is simply the previous number plus five.  Mathematically, X_n+1 = X_n + 5.  This means the next number (i.e., subscript n+1) in the pattern equals the last number in the sequence (i.e., subscript n) plus five.  So, in this case, you would predict the next three numbers are 25, 30 and 35.

 

Now, back to your original question.  Here, it's clear that there is no simple number that you can add or subtract to get the next number in the sequence.  So, instead of using addition/subtraction, you may need to use multiplication/division.  Do you see a number that you can multiply or divide 16 by and get 4?  Does this same number work in going from 4 to 1?  If so, you may have discovered the pattern.  Once you know this, you simply use this number and the proper operator (i.e., multiply/divide) to get the next 3 numbers in the pattern.

Answer 2

The common ratio is 1/4

16(1/4) = 1

1(1/4) = 1/4

 

1/16(1/4)= 1/64

1/64(1/4) = 1/256

1/256(1/4) = 1/1024