What number continues the pattern

Question

7, 16, 8, 27, 9, ?

Answer 1

7, 16, 8, 27, 9, ?, ...

 

Look at the odd-numbered terms:

 

7, 16, 8, 27, 9, ?

 

They are counting up by one starting at seven.  Based on that pattern, the next odd-numbered term would be 10:

 

7, 16, 8, 27, 9, ?, 10

 

Now look at the even numbered terms:

 

7, 16, 8, 27, 9, ?, 10

 

16 = 2*8 where 8 is the term that follows the 16.  27 = 3*9 where 9 is the term that follows 27.  Based on that rule, the ? would be 4*10 = 40. 

 

7, 16, 8, 27, 9, 40, 10, 55, 11, 72, 12, ...

 

There can be more than one rule that fits the limited data set.  For example, 16 = 4², 27 = 3³, so the ? entry could be 2⁴ which is 16 again.  That would be a correct answer as well, as long as you can establish a rule (pattern).

 

 

Answer 2

even-numbered positions seem to be 2⁴ and 3³ so one possibility is that the 6th item could be 4² which might be 16.

And possibly that would be a seventh number, ten because the odd-numbered positions are going up by 1.