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11.3 Geometric Sequences

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**Definition of a Geometric Sequence**

A geometric sequence is a sequence of the form Then number a is the first term, and r is the common ratio of the sequence. The nth term of a geometric sequence is given by

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Geometric Sequences If a=3 and r=2, then what is the nth term of the geometric sequence?

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**Finding terms of a Geometric Sequence**

Find the eighth term of the geometric sequence 5,15,45,…

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**Finding terms of a Geometric Sequence**

The third term of a geometric sequence is 63/4, the sixth term is 1701/32. Find the fifth term.

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**Partial Sums of a Geometric Sequence**

For a geometric sequence, the nth partial sum is given by

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**Finding a Partial Sum of a Geometric Sequence**

Find the sum of the first five terms of the geometric sequence 1,0.7,0.49,… Find the sum

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**Sum of an Infinite Series**

If |r|<1, then the infinite geometric series has the sum

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**Finding the Sum of an Infinite Geometric Series**

Find the sum of the infinite geometric series

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**Writing a Repeated Decimal as a Fraction**

Find the fraction that represents the rational number

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