Geometric Sequence,Means, and Infinite Geometric Sequence

Meer zoals dit

Spenst

door Mads Larsen

MATHEMATICS copy

door Charmaine Mendoza

overview page

door Helen Robinson

2014

door Marie Waddoups

Geometric Sequence,Means, and Infinite Geometric Sequence

Labels:

d=Distance

r=Common Ratio

n=The Number of Terms

an=The nth term

a1=First Term

Geometric Means

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

Infinite Geometric Sequence

Sum of an Infinite Geometric Sequence

Example: 2, 6, 18,... 3 15 75 r=3 a1=2 5 3 S= 2 3 1-3 5 S=5 3

Formula: s=a1 1-r Divergent=|r|>1 Convergent=|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

Formula: Sn=a1(1-r ) 1-r r=1 Sn=a1-an 1-r r=1

Geometric Sequence

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

Formula: an=a1(r)

What is Geometric Sequence -A sequence in which each term after the first term is obtained by multiplying.