SOLUTION: If geometric series 2,5+7,5+22,5+…=664300 determine the number of terms in the series

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(52864)   (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.

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