Back to: Further Mathematics SS1
Sequence & Series
A sequence is a pattern of numbers arranged in a particular order. Each of the number in the sequence is called a term. The terms are related to one another according to a well defined rule.
Consider the sequence 1, 4, 7, 10, 13 …., 1 is the first term,(T1) 4 is the second term(T2), 7 is the third term (T3).
The sum of the terms in a sequence is regarded as series. The series of the above sequence is
1 + 4 + 7 + 10 + 13 = 35
The nth term of a Sequence
The nth term of a sequence whose rule is stated may be represented by Tnso that T1, T2, T3etc represent the first term, second term, third term … etc respectively.
Consider the sequence 5, 9, 13, 17, 21 ……..
T1 = 5 + 4(0)
T2 = 5 + 4(1)
T3 = 5 + 4 (2)
T4 = 5 + 4 (3)
Tn = 5 + 4 (n – 1)
Tn = 5 + 4n – 4 = 4n +1
when n = 30
T30 = 4(30) + 1
T30 = 121
Find the nth term of these sequences:
(i) 3, 5, 7, 9 …… 2n + 1
(ii) 0, 1, 4, 9 ……… (n -1)2
(iii) 1/3, 3/4, 1, 7/6 ………………2n – 1
n + 2
Arithmetic Mean
If a, b, c are three consecutive terms of an A.P, then the common difference, d, equals
b – a = c – b = common difference.
b + b = a +c
2b = a + c
b = ½(a +c)
Examples
(i) Insert four arithmetic means between -5 and 10.
(ii) The 8th term of a linear sequence is 18 and the 12th term is 26. Find the first term, the common difference and the 20th term.
