1. 11.3 Geometric Sequences

2. 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

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

4. Finding terms of a Geometric Sequence
Find the eighth term of the geometric sequence 5,15,45,…

5. 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.

6. Partial Sums of a Geometric Sequence
For a geometric sequence, the nth partial sum
is given by

7. 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

8. Sum of an Infinite Series
If |r|<1, then the infinite geometric series has the sum

9. Finding the Sum of an Infinite Geometric Series
Find the sum of the infinite geometric series

10. Writing a Repeated Decimal as a Fraction
Find the fraction that represents the rational number