Geometric Sequence,Means, and Infinite 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 Answerundefined

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

Sn=a1-an
1-r r=1undefined

Example:
3,6,12,24,...,S10

n=10 r=2
a1=3

S10=3(1-2 )
1-2
=3(-1024)
-1
S10=3069=Final Answerundefined

Sum of an Infinite Geometric Sequence

Formula:
s=a1
1-r

Divergent=|r|>1
Convergent=|r|<1undefined

Example:
2, 6, 18,...
3 15 75

r=3 a1=2
5 3

S= 2
3
1-3
5

S=5
3undefined

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

a1=First Term

an=The nth term

n=The Number of Terms

r=Common Ratio

d=Distance