Geometric Sequence,Means, and Infinite Geometric Sequence
Geometric Sequence
What is Geometric Sequence
-A sequence in which each term after the first term is obtained by multiplying.
Formula:
an=a1(r)
Example:
1.)4,8,16,32,...,a12
a1=4 r=4
n=12 an=12
a12=4(2)
a12=4(2 )
a12=2048=Final Answer
Infinite Geometric Sequence
Formula:
Sn=a1(1-r )
1-r r=1
Sn=a1-an
1-r r=1
Example:
3,6,12,24,...,S10
n=10 r=2
a1=3
S10=3(1-2 )
1-2
=3(-1024)
-1
S10=3069=Final Answer
Sum of an Infinite Geometric Sequence
Formula:
s=a1
1-r
Divergent=|r|>1
Convergent=|r|<1
Example:
2, 6, 18,...
3 15 75
r=3 a1=2
5 3
S= 2
3
1-3
5
S=5
3
Geometric Means
Formula:
an=a1(r)
Example:
1.)2,10,50,250,1250
r=? n=5
an=1250 a1=2
Sn=1250=2r
1250=2r
1250=2r
2 2
625=r
5=r=Final Answer
Labels:
a1=First Term
an=The nth term
n=The Number of Terms
r=Common Ratio
d=Distance