Question

A pendulum swings 80 cm on its first swing, 76 cm on its second swing, 72.2 cm on its third swing, and 68.59 cm on its fourth swing. Complete parts a and b below.

a. If the pattern continues, what explicit formula can be used find the distance of the nth swing?

Answer 1

`a_(n) = 80*(0.95)^(n-1)`

Explanation:

Geometric sequences:

The nth term of a geometric sequence is given by the following equation.

`a_(n+1) = ra_(n)`

In which r is the common ratio.

This can be expanded for the nth term in the following way:

`a_(n) = a_(1)r^(n-1)`

In which
`a_(1)` is the first term.

In this question:

`a_(1) = 80, r = (68.59)/(72.2) = (72.2)/(76) = (76)/(80) = 0.95`

a. If the pattern continues, what explicit formula can be used find the distance of the nth swing?

`a_(n) = a_(1)r^(n-1)`

`a_(n) = 80*(0.95)^(n-1)`