Geometric Sequence,Means, and Infinite Geometric Sequence

Honelako gehiago

Sequences and Series Test

John Rodgers‑k egina

Sequences and Series Test

John Rodgers‑k egina

text stucture

jeremy flentge‑k egina

NUMBERS

Ilenia Fernandez‑k egina

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.