[Guest]

This one might be easy or hard if you see the trick to it or not. The task is to find the next number in the sequence, and also to explain the sequence. Please use the spoiler to hide answers.

4, 8, 9, 16, 16, 25, 27, 32, 64, 81, 125, 243, 256, 625, 1024, n

[Guest]

n= 3125 The sequence is the square,cube, fourth and fifth of the numbers 2,3,4 and 5 in numerical order

[fabpig]

Some numbers missing? 128, 512, 729?

Sorry...Ignore that...see you are only going as far as 5ths.

Edit...added apology!

Edited May 24, 2011 by fabpig

[Peekay]

3125

2,3,4,5 raised to the power of 2,3,4,5!

[Guest]

I am late for the answer...but yes it is 3125.

Consider all integer combinations of a^b for 2<=a<=5 and 2<=b<=5:

2^2=4, 2^3=8, 2^4=16, 2^5=32

3^2=9, 3^3=27, 3^4=81, 3^5=243

4^2=16, 4^3=64, 4^4=256, 4^5=1024

5^2=25, 5^3=125, 5^4=625, 5^5=3125

If they are then placed in numerical order, with any repeats removed, we get the following sequence of 16 distinct terms:

4, 8, 9, 16, 16, 25, 27, 32, 64, 81, 125, 243, 256, 625, 1024, 3125

[Aaryan]

3125

[Guest]

n= 3125 The sequence is the square,cube, fourth and fifth of the numbers 2,3,4 and 5 in numerical order

Excellent! Zeron solved it first and with the complete answer. And congrats to all who solved it.