13-3  Arithmetic and Geometric Series and Their Sums

Try the quiz at the bottom of the page!
go to quiz

Let's "walk" on thru some series and sums!!
  Important differences: 
Finite sequence: 1, 5, 9, 13, 17
Finite series: 1 + 5 + 9 + 13
Infinite sequence: 1, 2, 4, 8, 16, . . .
Infinite series:  1 + 2 + 4 + 8 + 16 + . . .
Note that a series is an indicated sum of the terms of a sequence!!  In this section, we work only with finite series and the related sums.
  How to find the sum of a finite Arithmetic Series!  
sn = n(t1 + tn)/2
To find the sum of a finite arithmetic series, you need to know three things. The first term, the last term and the number of terms.
Example problem:
To find the sum of a finite geometric series, you need to know three things:  the first term, how many terms to add and the common ratio!! (piece of cake!)
Example problem:

On to the next section!  We will begin out study of limits in the next section as related to infinite sequences.  I think we must be getting close to some calculus.  What do you think?  See you in the next section!
 
 

 
 
Current quizaroo #  13a
 
1)  Find the formula for tn only if it is an arithmetic sequence:  3, 7, 11, 15, 19, . . .
 
a)  not arithmetic
b)  tn = 4n - 1
c) tn = 3n + 1
d) tn = tn-1 + n
e) tn = 3n - 1
 
 
 
2)  Give the formula for tn only if it is a geometric sequence:  2, 5, 10, 17, 26, 37, . . . 

          a)  not geometric

b)  tn = n2 + 1
c)  tn = 2n + 1
d)  tn = tn-1 + 2n + 3
e)  tn = n2 - 1
 

 
 
3)  Find the recursive formula for the sequence:  3, 13, 33, 73, 153, . . .
 
a)  t1 = 3,  tn = tn-1 + 10n
b)  tn = 2tn-1 + 7
c)  t1 = 3,  tn = 2tn-1 + 7
d)  tn = 3 + 10n
e)  There is no formula
 
 
 
4)  Find the sum of the arithmetic series:  S50;  6 + 12 + 18 + 24 + 30 + . . . 
 
a)  15300
b)  306
c)  153
d)  7500
e)  7650

 
 
  5)  Find the sum of all the multiples of 4 between 1 and 999.       
 
a)  249  
b)  249000
c)  124500
d)  1000
e)  124002
 
 

 click here for answers!!