Geometric Sequence
 A sequence such as 1,2,4,8,........1024 or 2,6,18,54...........118098 which has a constant ratio between terms.
 The first term is written as a_{1},
 The second term is written as a_{2},
 The third term is written as a_{3},
 The fourth term is written as a_{4},
 The fifth term is written as a_{5}, ....
 The tenth terms is written as a_{10} and
 The ratio as r
Examples:
 1,2,4,8,........1024 = 1x2^{0} , 1x2^{1} , 1x2^{2} , 1x2^{3},........
 2,4,8,16,32........1024 = 2x2^{0} , 2x2^{1} , 2x2^{2} , 2x2^{3},........
 1,3,9,27,........ = 1x3^{0} , 1x3^{1} , 1x2^{3} , 1x2^{4},........
 4,16,64........= 1x4^{1} , 1x4^{2} , 1x4^{3},........
 7,21,63........= 7x3^{0} , 7x3^{1} , 7x3^{2},........
 10,100,1000,10000,....... = 1x10^{1}, 1x10^{2}, 1x10^{3}, 1x10^{4}.............
 2,4,8,........1024
The first term is a_{1}, the 5th term as a_{5}, the 10th terms as a_{10} and the ratio as r.
a_{1}r^{0}
a_{2} = a_{1} r^{1}
a_{3} = a_{2 }r^{1} = (a_{1} r^{1}) r^{1} = a_{1} r^{2}
a_{4} = a_{3} r^{1} = (a_{2}r^{1}) r^{1} = a_{1} r^{3}
a_{5} = a_{1} r^{4}
a_{6} = a_{1}r^{5}
a_{7} = a_{1} r^{6}
........
a_{n} = a_{1}r^{n1}
The formula to find the n^{th} term in geometric series is
Example:
Power notation:

1=10^{0}, 10 = 10^{1}, 100 = 10^{2}, 1000 = 10^{3}, 10000 = 10^{4}............
 1 = 2^{0}, 2=2^{1}, 4=2^{2}, 8=2^{3}, ............1024=2^{10}
Let the first term be a_{1}
the 5th term be a_{5}
the 10th term be a_{10}
ratio be r
a_{1} = 2^{0}
a_{5} = 2^{4}
a_{10} = 2^{9}
r = 2
 1 = 3^{0}, 3=3^{1}, 9=3^{2}, 27=3^{3}, ............59049=3^{10}
2 = 2x3_{0}
6 = 2x3^{1}
18 = 2x3_{2}
54 = 2x3^{3}
...........
118098=2x3^{10}
Term Number  1  2  3  4  .....  n 
Term of Geometric Series 
a_{1} 
a_{2} 
a_{3} 
a_{4} 
..... 
a_{n} 
Term of Geometric Series 
a_{1} r^{0} 
a_{1}r^{1} 
a_{1}r^{2} 
a_{1}r^{3} 
..... 
a_{1} r^{n1} 
Example 
2x3^{0} 
2x3^{1} 
2x3^{2} 
2x3^{3} 
........... 
2x3^{n1} 
More Examples:
Geometric Sequence  Common Ratio 
3, 1, 1/3, 1/3^{2}, 1/3^{3},. . . .  1/3 
2, 2Ö3, 6, 6Ö3, 18 . . . .  Ö3 
 
Directions: Find r, a_{1}, a_{5}, a_{101} for the following arithmetic sequence. Also write at least 5 examples of your own.
