Posted by ll on .
An arithmetic series has a first term of 4 and a common difference of 1. A geometric series has a first term of 8 and a common ratio of 0.5. After how many terms does the sum of the arithmetic series exceed the sum of the geometric series?

math studies 
ll,
anyone????

math studies 
ll,
please

math studies 
ll,
can anyone help?

math studies 
Reiny,
for the AS
S_{n} = n/2(8 + n1)
= n/2(n9)
for a GS
S_{n} = 8(1.5^n)/(1.5)
so n/2(n9) > 8(1.5^n)/(1.5)
n/2(n9) > 16(1.5^n)
n^2  9n > 32  32(.5^n)
32(.5)^n + n^2  9n  32 > 0
set it equal to zero and attempt to solve it.
This would be a very nasty equation to solve, except you know that n has to be a whole number, so do some trial and error calculations.
eg. n = 2 we get 38 > 0 which is false
if n = 5 we get 44 > 0 which is false
if n = 20 we get 188 > 0 which is true
So somewhere between n=5 and n=20 there should be a solution
(n=12 > 4.0078 > 0 mmmmhhh?)