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Alexeev081 [22]
2 years ago
11

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 sw

ing. Complete parts a and b below.
a. If the pattern continues, what explicit formula can be used find the distance of the nth swing?
Mathematics
1 answer:
Kisachek [45]2 years ago
7 0

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}

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