Question

What is the common ratio r?

Answer 1

The graph shows the first three terms in a
geometric sequence.

Answer 2

if n=1, then a1 = 2
if n=2, then a2 = 5
if n=3, then a3 = 25/2

yeah, it is a geometry sequence
with r (ratio) = a2/a1 = 5/2
or you can take r = a3/a2 = (25/2)/5 = 25/10 = 5/2

Answer 3

does that make sense ?

Answer 4

Yes it does. How would I find the recursive formula for the sequence?

Answer 5

use the general formula of geo sequence :
an = a1 * r^(n-1)

with a1 = 1st term = 2 and
r is known = 5/2

therefore,
an = a1 * r^(n-1) = 2 * (5/2)^(n-1) = 2 * (5/2)^n * (5/2)^(-1)

just simplify that, get
an = 2 * (5/2)^n * (5/2)^(-1)
an = 2 * (5/2)^n * (2/5)
an = 4/5 * (5/2)^n

Answer 6

Ohhhhhhhhh , OK. that makes sense