Step-by-step explanation:
a geometric sequence means every new element is created by multiplying the previous element always with the same number.
a n = a n-1 * number
a n = a1 * number^(n-1)
=> a8 (or g(8)) / a3 (or g(3)) = number^5 (5=8-3)
=> 32/1 = number^5
=>
[tex]number = \sqrt[5]{32} [/tex]
number = 2
and what is the starting a1 ?
it must satisfy e.g. a3
1 = a1 * 2^2
=> a1 = 1/4
therefore, the requested definition looks like
g(1) = 1/4
g(n) = g(n-1) * 2
