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.

1
by mishiee

2015-03-31T21:28:16+08:00

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Given:
A geometric series problem.
1st term = 18 inches
Common ratio =  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:

Where:
S - means "sum."
n - means "number of terms."
- means "sum of the first "blank" number of terms."
r - means ratio
- means 1st term

Let us solve! ;)

We just substitute the formula.

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.