
UNIT
10 :
SEQUENCES AND SERIES
LESSON 3:
ARITHMETIC SERIES
Arithmetic
Series:
Recall a sequence such as –2, 3, 8, 13, …
is called an Arithmetic Sequence.
These sequences have the following properties.
·
Terms
are denoted as t_{1} , t_{2} , t_{3 , }referring
_{ }to term1, term 2,
term 3 …
·
The difference between successive terms is constant. ie t_{2}
– t_{1} = t_{3} – t_{2} = t_{4} – t_{3}
etc
·
This
difference is called the common
difference and denoted
using the letter d. Here d
= 5.
·
The
first term is denoted using the letter a. Here a = 2.
·
Successive
terms are found by adding the common difference, d, to the preceding
term. Hence t_{5} = 13 +
5 = 18 etc.
·
The
formula for the general term or nth term is t_{n }= a + (n
– 1)d
Definition: The sum of the terms of an
arithmetic sequence is an Arithmetic Series.
Example 1: Given the first
few terms.
For the arithmetic series below, above, find t_{11}, the general term t_{n} and the sum of 40 terms S_{40.}
Solution:
a = 1 d = 3 n = 11 t_{n} = ? S_{40} = ?
Example 2: Given the first
and last terms.
a =  3 d =  4 t_{n} =  219 n = ? S_{n} = ?
Solution:
Example 3: Given two terms.
The
fourth and seventh terms of an arithmetic series are 8 and 17
respectively. Find a, d and S_{26}.
Solution: