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Write a rule for the nth term of the geometric sequence if r = 1/4 and a3 = 2.

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6 votes

Answer:


a_(n) = 32((1)/(4))^(n-1)

Explanation:

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.

This means that for example:


a_(3) = a_(1)r^(3-1)

So


a_(3) = a_(1)r^(2)


2 = a_(1)((1)/(4))^(2)


2 = (a_(1))/(16)


a_(1) = 32

Then


a_(n) = 32((1)/(4))^(n-1)

User Chris Colbert
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