For the geometric sequence 1,2,4 find a8

First, create a rule for this sequence.

Let a(1) be the first term (which here happens to be 1).

The next term, a(2), is twice the previous term, that is, twice 1, or 2.

a(3) = 2a(2) = 2(2) = 4

This is called a "recursive function."

The 3rd term is 4.  The next, which is a(3) is 2*4, or 8.

Note that there's an alternative approach.  The first term, a(1), is 1; the next is a(2) = a(1)*2^(2-1)   =  1*2^1=2
the next is a(3) = 1*2^(3-1) = 1*2^2 = 4

So the rule is   a(n) = a(1)*2^(n-1).

So a(8) is a(1)*2^(8-1)   =    1*2^7  = 2^3*2^4  =   8(16) = 128