Question

How do you find the explicit formula for: 1, 2, 4, 8...?

Answer 1

`a_n = 2^(n-1)`

Explanation:

The difference between successive terms is not a constant,
so the sequence is not an arithmetic sequence.

Checking to see if the sequence might be geometric,
we see the successive terms are all a multiple of `2` times the previous term.

`a_1=1=2^0`
`a_2=a_1xx2=2^1`
`a_3=a_2xx2=a_1xx2^2 = 2^2`
`a_4=a_3xx2=a_1xx2^3=2^3`

so we could generalize:
`color(white)("XXX")a_n=2^(n-1)`