Asked by tom

sum of the geometric series (2 - 3^n) / 5^n

whats a and r?
Answered by tom
its an infinite series by the way
Answered by oobleck
The series is not geometric, as there is no common ratio.
However, it is the difference of two geometric series
(2-3^n)/5^n = 2/5^n - 3^n/5^n = 2(1/5)^n - (3/5)^n
The first series has a = 2/5 and r=1/5
The second series has a = 3/5 and r = 3/5
Now just find the sum of each as usual, and subtract.
Answered by tom
so s=0?
Answered by oobleck
no. what is your work?
Just plug in S∞ = a/(1-r)
Answered by tom
i did (2/5)^n and i got 5/2. I did (3/5)^n and i got 5/2. 5/2 - 5/2 = 0
Answered by oobleck
(2/5) / (1 - 1/5) = (2/5) / (4/5) = 1/2
(3/5) / (1 - 3/5) = (3/5) / (2/5) = 3/2
1/2 - 3/2 = -1

You showed some work, but you didn't use the values for a and r that I showed you!
Answered by tom
how did you get your a and r?
Answered by oobleck
geez - write down the first few terms of each of the geometric sequences.
There are no AI answers yet. The ability to request AI answers is coming soon!