## Geometric sequence

A geometric sequence is one in which the same number is multiplied by each number in the sequence of numbers to get the next number in the sequence. Here are some examples of geometric sequences:

 `2   4   8   16 ... ` <== Each term is multiplied by 2 to get the next term in the sequence `1 1/2 1/4 1/8 1/16 ...` <== Each term is multiplied by 1/2 to get the next term in the sequence `2   -4   +8   -16 ...` <== Each term is multiplied by -2 to get the next term in the sequence.   (Remember that -4 x -2 = +8)

Here are some common geometric sequence problems:
 Find the Nth term of a geometric sequence Find the sum of the first N terms of an a geometric sequence: An = A1 x m (n - 1)   where:     A1 is the first term,     An is the nth term (the term you are looking for)     m is the number that each term is multiplied by to get the next term. So, the 5th term of the first sequence above       (2, 4, 8, . . .) is: A5 = 2 * 2(5-1) = 2 * 2(4) = 2 * 16 = 32 Sum = A1 [ (1 - m n) / (1 - m)]     A1 is the first term     m is the number that each term is multiplied         by to get the next term. So, the sum of the first 4 terms of the first sequence above (2,4,8 ...) is Sum = 2 (1-24)  / (1 - 2) =             2 (1-16) / (-1) =             2 (-15)   / (-1) = 2 x 15 = 30             (2+4+8+16 = 30)
Note: If you have a sequence where the same number is added to or subtracted from each term to get the next one, you have an arithmetic sequence.
Here are some questions for you:
Hint: Use the xy key on your calculator
1. What is the next number in this sequence?     3   9   27   ___

2. What is the 10th term of that sequence? _____

3. What is the sum of the first 5 terms of this sequence:
Sum = 3 ( 1 - 35) / (1 - 3) =

Sum = ____________
Note: It's a good idea to memorize the prime numbers up to 100:
2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97