A geometric series is a series of the form
a_0+a_0r+a_0r^2+a_0r^3+...
where a_0 is the initial term and r is the common ratio between terms. We can easily find r by dividing any term after the first by the prior term. So in this case we have
a_0=100 and r = 99/100=0.99
Now, looking at the general form of the series, we can see that the n^"th" term has the form a_0r^(n-1). Thus, as we have the last term in the series, we simply need to solve for n for that term to find the total number of terms.
36.97=a_0r^(n-1)=100(0.99)^(n-1)
=>0.3697=0.99^(n-1)
=>ln(0.3697)=ln(0.99^(n-1)) = (n-1)ln(0.99)
=>n=ln(0.3697)/(ln(0.99))+1 ~~ 100
Thus there are 100 terms in the series.
