UNIT 10 : SEQUENCES AND SERIES
LESSON 3: 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 t1 , t2 , t3 , referring to term1, term 2, term 3 …
· The difference between successive terms is constant. ie t2 – t1 = t3 – t2 = t4 – t3 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 t5 = 13 + 5 = 18 etc.
· The formula for the general term or nth term is tn = 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 t11, the general term tn and the sum of 40 terms S40.
a = 1 d = 3 n = 11 tn = ? S40 = ?
a = 1
d = 3
n = 11
tn = ?
S40 = ?
Example 2: Given the first and last terms.
a = - 3 d = - 4 tn = - 219 n = ? Sn = ?
a = - 3
d = - 4
tn = - 219
n = ?
Sn = ?
Example 3: Given two terms.
The fourth and seventh terms of an arithmetic series are 8 and 17 respectively. Find a, d and S26.