11.3 Geometric Sequences

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

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

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

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.

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

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

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

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

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