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