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

Answer:

$a_{n} = 80*(0.95)^{n-1}$

Step-by-step 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:

$a_{1} = 80, r = \frac{68.59}{72.2} = \frac{72.2}{76} = \frac{76}{80} = 0.95$

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

$a_{n} = a_{1}r^{n-1}$

$a_{n} = 80*(0.95)^{n-1}$