To calculate : the distance a pendulum swings if the pendulum travels 10 inches on its first swing. On each succession the pendulum travels
The total distance a pendulum swings is
Given information :
The pendulum travels 10 inches on its first swing. On each succession the pendulum travels
Formula used : The sum of infinite geometric series with first term
Here,
Calculation :
It can be observed that the person swings by one swing and every next swing is equal to
On the first swing the person travels distance of
So,
On the second swing, the person travels
So,
Similarly,
It can be seen that, the sequence forms a geometric sequence with value of
Observe all the terms as follows.
The general rule for the given geometric sequence is formed as
For the given series the value of
The sum of series can only exist if the common ratio is
Then the sum of infinite geometric series is calculated using the formula
Thus, the total distance a pendulum swings is
Chapter 7 Solutions
Holt Mcdougal Larson Algebra 2: Student Edition 2012
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