Business
Mathematics
Course Code: MGSC 101
Lecture 3
Sequences and Series
Two types :
st
nd
3
rd
2
---th
1000
---2001
???
x1 0 0 0  3  2 (1 0 0 0  1)
x1 0 0 0  2 0 0 1
x 9  3  5 (9  1)
x9  4 3
Example :
x 1 0  4  d (1 0  1)
a = 4 , x10=67
67  4  9d
d 
63
9
d  7
The values of a and d are:
a = -12 (the first term)
d = 5 (the "common difference")
So,
x32 = -12+5(32-1) = 143
Sn 
n
2
 x1
Example :
 xn

n
Term
1ST
1
2nd
2
3rd
4
-----
-----
x 20  1  2
20
524288
x 20  2
???
19
2 0 1
 524288
Example :
a 3
r  2
x1 1  3   2 
1 11
x1 1  3 0 7 2
a  81
r 
1
3
1
x9  8 1   
3
x9 
1
81
9 1
Gn 
If the common ratio, 𝑟, satisfies |𝑟| < 1, then the sum of an
infinite geometric series with first term 𝑎 is: