Question 1200344: If geometric series 2,5+7,5+22,5+…=664300 determine the number of terms in the series
Found 2 solutions by htmentor, ikleyn:
Answer by htmentor(1343)   (Show Source):
You can put this solution on YOUR website! The nth term of a geometric series is a_n = a*r^(n-1), where a is the 1st term
and r is the common ratio. Here we have a = 2.5 and r = (7.5/2.5) = 3.
The sum of the 1st n terms S_n = a*(1-r^n)/(1-r).
S_n = 2.5*(1-3^n)/(1-3) = 664300 = -1.25*(1-3^n) -> 3^n = 531441.
Take log3 of both sides:
n = log3(531441) = 12.
Ans: 12 terms
Answer by ikleyn(52861)  (Show Source):
You can put this solution on YOUR website! .
By the way and for your info:
In Math, 2,5 is not a number: such writing represents TWO numbers, separated by comma.
If you want to represent ONE number 2 as a decimal, write 2.5
(using decimal point, or "dot").
A comma is used in Math writing for TOTALLY DIFFERENT purposes.
|
|
|
