Mishieeidn
Answered

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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.

Sagot :

Jeremiaidn
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].


                       
          

                         
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