Given:
A geometric series problem.
1st term = 18 inches
Common ratio = [tex] \frac{3}{4} [/tex] or 0.75
There are 5 terms in this series.
The sum should be rounded to the nearest tenths.
Find:
Total distance covered by the pendulum in its first five swings.
Solution:
Formula for Geometric Series:
[tex]S_{n} =[/tex] [tex] \frac{t _{1}(1-r^{n}) }{1-r} [/tex]
Where:
S - means "sum."
n - means "number of terms."
[tex] S_{n} [/tex] - means "sum of the first "blank" number of terms."
r - means ratio
[tex] t_{1} [/tex] - means 1st term
Let us solve! ;)
We just substitute the formula.
[tex]S_{n} = [/tex] [tex] \frac{ t_{1}(1- r^{n}) }{1-r} [/tex]
[tex]S_{5} = [/tex] [tex] \frac{18 (1- 0.75^{5}) }{1-0.75} [/tex]
[tex] S_{5} =[/tex] [tex] \frac{18(1-0.2373046875)}{0.25} [/tex]
[tex] S_{5} =[/tex] [tex] \frac{18(0.7626953125)}{0.25} [/tex]
[tex] S_{5} =[/tex] [tex] \frac{13.728515625}{0.25} [/tex]
[tex] S_{5} =[/tex] 54.9140625
At this point, we should not forget that the answer should be rounded off to the nearest tenths. and of course, the units which is in inches.
Answer:
The total distance traveled by the pendulum during the first five swings is [tex]54.9 [/tex] [tex]inches[/tex].
