Page 94 - Mathematics_Form_3

Sequences and series

In a simple infinite series, the general Example 4.7
term can be found by studying few terms Consider the sequence 1, 3, 5 , 7, . . .
of the given series. For instance, the
(a) Find the general term of the
terms of the series 10 + 20 + 30 + 40 + ···
are multiples of 10, such that: sequence.
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the first term is 1 × 10, with n = 1; (b) Write its corresponding series.
the second term is 2 × 10, with n = 2; (c) Find the sum of the first five terms.
and the third term is 3 × 10, with n = 3.
Solution
th
This implies that the n term is n × 10. (a) For the sequence,
Therefore, the series The 1 term: 1 = 2 × 1 − 1
st
10 + 20 + 30 + 40 + ··· can also be The 2 term: 3 = 2 × 2 − 1
nd
written as rd
10 + 20 + 30 + 40 + ··· + 10n. The 3 term: 5 = 2 × 3 − 1
th
The 4 term: 7 = 2 × 4 − 1
Example 4.6 ⋮ ⋮
th
The n term: 2 × n − 1 = 2n − 1 .
Consider the sequence Therefore, the general term is
2, 4, 6, 8, 10, 12, . . .
2n − 1.
th
(a) Write the n term.
(b) The corresponding series is
(b) Write the series corresponding to
1 + 3 + 5 + 7 + · · · + (2n − 1).
the sequence.
(c) Find the sum of the first four terms. (c) The first five terms are
1, 3, 5, 7, 9 whose sum is
Solution
(a) For the sequence, 1 + 3 + 5 + 7 + 9 = 25.

1 term: 2 = 21× ,
st
2 term: 4 22= × , Exercise 4.2
nd
3 term: 6 = 23× and 1. If the general term of a certain
rd
th
n term: 2n, sequence is 2( 1)− n , Mathematics for Secondary Schools
Therefore, general term is 2n. (a) write its series.
(b) find the sum of the series up to
(b) The series corresponding to the the sixth term.
given sequence is 2. Find the n term of the series
th
...
2 + 4 + 6 + 8 + 10 + 12 + + 2n . + + + + · · ·
3 __
2 __
1 __
4 __
(c) Since the first four terms are 2 3 4 5
2, 4, 6 and 8, their sum is 3. Find the sum of the first ten terms
2 + 4 + 6 + 8 = 20. of the series − 4 − 1 + 2 + 5 + · · ·

Student\s Book Form Three 87

18/09/2025 09:59:19
MATHEMATIC F3 SB.indd 87 18/09/2025 09:59:19
MATHEMATIC F3 SB.indd 87