Question

Find the sequence.. 1,2,2,4,8

Answer 1

Let the n-th term be called $a_n$

We see that if we choose $a_0=1,a_1=2$ then the other numbers follow the pattern $a_{n+2}=a_{n+1}\cdot a_n$ (see :$4=2*2,8=4*2$)

Hence the sequence will be $1,2,2,4,8,32,256, 8192, 2097152, 17179869184,\dots$