In succession 8, 32, 128 what number is next?

This is a geometric sequence because each term is a common ratio of the previous term.  In this case the common ratio is 4...

32/8=128/32=r=4

Any geometric sequence can be expressed as:

a(n)=ar^(n-1), a(n)=nth term, a=initial term, r=common ratio, n=term number.

In this case a=8 and r=4 so

a(n)=8(4^(n-1))  so the 4th number would be:

a(4)=8(4^3)

a(4)=8(64)

a(4)=512

Now obviously we could have just said a(4)=4*128, but you rarely are asked for the next number as it is pretty obvious,  The above steps and reasoning are what you will need in the majority of questions about geometric sequences...

With a continuous thought process.