If the sequence 36, 24, 16, ... is geometric, find S5. PLEASE I NEED HELP W THIS!!

108
Explanation:
In any geometric series, we need two pieces of information to find its sum to the
n
-th term, and thus the sum to infinity.
Firstly, we need the first term,
a
. This is obviously
36
in this expression.
Secondly, we need the common ratio,
r
,. We find this by taking 24/36 =2/3
Thus a =36 and r =2/3 . also note that
(R) =2/3 <1

We then apply the formula for sum of geometric series to the
n -th term when (r) <1 : Sn =a(1 -rn ) / 1-r = 36 ( 1 - (2/3 ) n) / 1 -(2/3)
=108 (1 -(2/3) n)
The sum to infinity s ♾ is defined to be the limit of sn as n - ♾
N- ♾,(2/3) n -0.sn -108 -0 =108
S ♾ =108

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