Geometric Sequence,Means, and Infinite Geometric Sequence

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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.