Series and sequence problem. Pls help me
very appreciated.
On the first swing, the length of the arc through which a pendulum swing is 18 in. The length of each successive swing is 3/4 of the preceding swing. What is the total distance the pendulum has traveled during the first five swings? Round to the nearest tenth.




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              A geometric series problem.
              1st term = 18 inches
              Common ratio =  \frac{3}{4} or 0.75
              There are 5 terms in this series.
              The sum should be rounded to the nearest tenths.

           Total distance covered by the pendulum in its first five swings.

                Formula for Geometric Series:
                         S_{n} =  \frac{t _{1}(1-r^{n})  }{1-r}

            S - means "sum."
            n - means "number of terms."
           S_{n} - means "sum of the first "blank" number of terms."
            r - means ratio
            t_{1} - means 1st term
Let us solve! ;)
  We just substitute the formula.

          S_{n} =    \frac{ t_{1}(1- r^{n})  }{1-r}

          S_{5} =  \frac{18 (1- 0.75^{5}) }{1-0.75}

           S_{5} =  \frac{18(1-0.2373046875)}{0.25}

           S_{5} =  \frac{18(0.7626953125)}{0.25}

           S_{5} =  \frac{13.728515625}{0.25}

           S_{5} = 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.

                      The total distance traveled by the pendulum during the first five swings is 54.9  inches.