Hi! When I completed this question I used an alternate pattern which appears to work too.

The question reads:

What should the next number in this sequence be?

1 2 9 64 ??

The way I answered it was as follows:

n sub q = the value of a a given term in the sequence (i.e. n sub q=1, 2, 9,...., ??, depending on q. Sorry for the weird notation, but I'm not sure how to make subscripts on my phone so I have to use sub q)

q = term of the sequence (q=1, 2, 3, 4.... So when q=3, n=9 or in other words, n sub (q=3) = 9)

You can find any number in the sequence by using this formula:

n sub (q+1) = (n sub q)(1+3(q-1))+1

n sub (1+1) = (1)(1 + 0) + 1 = 2

n sub (2 + 1) = (2)(1 + 3(2 - 1)) + 1 = 9

n sub (3 + 1) = (9)(1 + 3(3 - 1)) + 1 = 64

n sub (4 + 1) = (64)(1 + 3(4 - 1)) + 1 = 641

This can also be used to work backwards if, for example, you weren't given that n sub 1 = 1.

Thanks for your help and I look forward to hearing back!