Page 93 - Mathematics_Form_3

Sequences and series

2. Use the matchsticks to form shapes In the previous section, you learnt
as shown in Figures 4.2 (a), (b), that, when a set of terms is written in
and (c). a definite order and there is a rule by
which the terms are obtained, then the
FOR ONLINE READING ONLY
set of terms is called a sequence. When
the terms of a sequence are connected
by addition or subtraction signs, the
resulting expression is called a series or
Figure 4.2(a): A whole square progression. The following are examples
of series:

(a) 1 + 2 + 3 + 4 + · · · + 50.

(b) 2 + 4 + 6 + 8 + · · · + 20.

(c) 1 + − 1 + 1 + − 1 + · · ·
Figure 4.2(b): A whole rectangle divided
1 _
1 __
1 __
1 __
into 2 equal parts (d) + + + + · · ·
2 3 4 5
(e) − 2 − 4 − 6 − 8 − 10 – · · ·
A series can be finite or infinite. If a
series ends after a finite numbers of
terms, the series is said to be finite.
Figure 4.2(c): A whole rectangle divided However, If a series does not have an
into 3 equal parts
end it is called an infinite series. Thus,
3. As you form the shapes, count the 1 + 2 + 3 + 4 + 5 is a finite series while
Mathematics for Secondary Schools 4. Use the pattern to determine how Sum of the first n terms of a series
number of matchsticks used. You
1 + 2 + 3 + 4 + 5 + · · · is an infinite
can keep on forming the shapes and
series.
study the nature of the pattern as
you increase the number of shapes
th
and the number of matchsticks.
Consider a series having n terms. The
many matchsticks you would need sum of all the n terms of the series is
usually denoted by S . Thus, the sum
to make a figure of 10-squares.
n
5. If you are to make a figure of
n-squares, how many matchsticks be written as S = 1 + 2 + 3 + 4 +
n
would you need? of 1 + 2 + 3 + 4 + 5 + 6 + · · · + n can
5 + 6 + · · · + n. In this case, n is the
6. Share your final work with other general term or the last term of the finite
students for further discussion. series 1 + 2 + 3 + 4 + 5 + 6 + · · · + n.

86 Student\s Book Form Three

18/09/2025 09:59:19
MATHEMATIC F3 SB.indd 86
MATHEMATIC F3 SB.indd 86 18/09/2025 09:59:19