Question

In a geometric sequence, g(3) = 1 and g(8) = 32. Which recursive definition produces this geometric sequence?

Answer 1

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

=>

$number = \sqrt[5]{32}$

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