Find an explicit formula for the geometric sequence 120, 60, 30, 15, ....
Mathematics · Middle School · Tue Nov 03 2020
Answered on
Given the geometric sequence:
120, 60, 30, 15, …
In order to determine the formula of the given geometric function, we must first determine the ratio between each term. This can be done by dividing the second term with the first term.
r= 60/120
r = 0.5
since we already know the ratio between each term, we can simply write the equation.
a(n) = a1 ( r )^(n-1)
In order to check if the equation is true, we substitute n with 2 to see if the answer is 60.
a(2) = 120 ( 0.5 )^(2-1)
a(2) = 120 ( 0.5 )
a(2) = 60
a(3) = 120 ( 0.5 )^(3-1)
a(3) = 120 ( 0.25)
a(3) = 30