Upload
philip-stephens
View
218
Download
0
Embed Size (px)
Citation preview
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 + …