Lesson # 17: Geometric Sequences & Series

Formula:

tn = ar^n-1
tn - value
n - the position
r - multiplier (2nd/1st)

Example:             2, 6, 18, 54,......
1) t10
tn = 2(3)^9
tn = 39 366

2) How many terms are in the following sequence?   8, 12, 18, 27,...... 205.03125
205.03125 = 8(1.5)^n-1
        8                  8
log(25.6289) = (n-1) log(1.5)
   log(1.5)             log(1.5)
8 = n-1     
9 = n


Series:
 A series is the sum of a sequence
S= add   t= find number

Formula:
 
Sn = a(1 - r^n)   or   Sn = a- rl                           
             1-r                       1-r      
 
Sn: series (sum)       
r: ratio     
l: last term> tn
a: first #         
n: how many terms there is

Example:
1) Find the sum of the series          5 + 15+ 45 +.......... + 885 735
Sn =  a - rl
          1-r               
Sn= 5 - 3(885 735)
             1-3                                                                                      
     =  1, 328, 600