Section 12-4

-Finding sums of geometric series

-Using Sigma notation

Taylor Morgan

Vocab.• Geometric Sequence-(From previous section)

sequence in which each term after the first is found by multiplying a ratio, known as the common ratio, r, to the previous term

• Series- an indicated sum of the terms in a sequence

• Geometric series- an indicated sum of the terms in a geometric sequence

• Ex. 1) 18, 9, 4.5 Ex.2) 4+8+16+32 Ex. 3) -9, 3,-1 Ex.4) 3/8+ 3/16 + 3/32

Geometric Sequence Geometric Series

Terms in a Series

• represents the sum of the first n terms in a series

• So, for example, is the sum of the first four terms

Ex. For the series ½ +1+2+4, is

½ + 1 + 2 + 4 is 7.5

nS

4S

4S

Where:

r= the common ratio by dividing two consecutive terms

n= number of terms

a = 1st term in a series

a = nth term in a series

1

n

Sum of an Geometric Series

• The sum of the first n terms of an arithmetic series is given by

nS

Find the Sum of an Geometric Series

Given the following formula:

• Find the sum of the first

• 5 times of the geometric

• Sequence:

• 100 + 20 + …