10,21,45,99,?

225

How did you come up with answer?

Another good example of how giving just an answer doesn't help anyone... Sigh.

Well, what I came up with;

10, 21, 45, 99, ___

2*5, 3*7, 5*9, 9*11, ___

The second number is increasing by 2, see? 5, 7, 9, 11,. So, the next is 13.

The first number; 2, 3, 5, 9,. hmmm that's like +1, +2, +4, maybe the next one is +8, so, that will be 9+8 = 17.

So I think that the next number is 17*13 = 221.

Oh, I now I came up with another answer... that of joseph :p

First term times 2, then add 1 ({10*2} +1)= 21
Then, times 2, plus 3 ({21*2}+3) = 45
Then, times 2, plus 9 ({45*2}+9) = 99
Then, times 2, plus 27 ({99*2} +27) = 225

Both answers seem correct to me though :)

They asked what was next. This might be homework, I wanted them to think.

My answers are never that short.

Good day to all.

Thanks for all your answers!
I had to dig through some of my old college math books to find adjacent sequences.
My answer is as shown:
a(n) = [ a(n-1)/a(1) + a(n-1)/a(2) +... + a(n-1)/a(n-1) ] for n >= 3. +0
2

10, 21, 45, 99, (219)

Sorry, this is not homework,I'm over 50.
It was a bonus question on a test that my wife had taken at work and asked me for the answer to see if she had answered it correctly.
Thank Everyone Again
Charles