Question 1200344
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