Answer:
127.75
Step-by-step explanation:
The sum of first "n" terms of a geometric series is given by the formula:
[tex]S_n=\frac{a(1-r^n)}{1-r}[/tex]
Where
a is the first term
n is the number of term
r is the common ratio
The first term is 64, so
a = 64
We want first 9 term's sum, so
n = 9
To get common ratio, we divide 2nd term by 1st term, so
32/64 = 1/2
r = 1/2
Now, substituting in formula we get our answer:
[tex]S_n=\frac{a(1-r^n)}{1-r}\\S_9=\frac{64(1-(\frac{1}{2})^9)}{1-\frac{1}{2}}\\S_9=\frac{511}{4}\\S_9=127.75[/tex]
The sum of the first 9 terms of this geometric series is 127.75
