7,16,9,5,21,16,9,?,1

Question

is it 10 or 13 or 5?

 

Answer 1

7, 16, 9, 5, 21, 16, 9, , 1

 

break this into groups of 3 numbers

to see the pattern.

7, 16, 9... 16-7=9

5, 21, 16... 21-5=16

9, x, 1... x-9=1 ... x=10

 

however, the others are correct that this neither an arithmetic sequence nor a geometric sequence.  There is no way to determine what number will come after the 1.

Answer 2

A sequence of numbers has some relationship from the previous one(s) to the next one(s).

 

We usually test the common ones, then go on to the more unusual ones:

7,16,9,5,21,16,9,?,1  is not an Arithmetic Sequence since there is not a common difference.

7,16,9,5,21,16,9,?,1  is not a Geometric Sequence since there is not a common ratio.

 

Now, for any set of numbers, there is one or more possible explanations for them.  So, we start looking.

 

How about this:

 7 = 16 - 9

 5 = 21 - 16

 9 = 10 - 1

 

Given the choices, I'd guess that the answer is 10.

Answer 3

It's anybody's guess!