Page 90 - Mathematics_Form_3

Sequences and series

Number of In general, a pattern is a rule which
hexagons 1 2 3 4 5 6 helps to find other numbers in a given
list. A member of a particular pattern is
Number of
matchsticks 6 11 called a term. Each term has its particular
position; a term in the first position is
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3. How many matchsticks are required called the first term, a term in the second
to make a shape similar to that in position is called the second term, and
Figure 4.1 with: so on. Using such names, a term in the
th
(i) 8 hexagons? n position is called the n term or the
th
(ii) 16 hexagons? general term and is denoted by U .
n
(iii) 100 hexagons? The order in which terms appear in a
4. Explain how you arrived at the certain pattern is important. For instance,
answers in tasks 2 and 3. the pattern 1, 2, 3, 4, . . . is completely

5. Explain using an equation if different from the pattern 4, 3, 2, 1, ...
possible, how you can find the because they have different ordering.
number of matchsticks for any Sequences are either finite or infinite. A
number of hexagons you can make.
sequence with a limited number of terms
6. Present your final work to the rest is called a finite sequence. For instance;
of the class for further discussion − 9, − 6, − 3, 0, 3, 6, 9 is a finite sequence,
and inputs. while a sequence with unlimited number
of terms is called an infinite sequence.
There are sets of numbers with simple For instance; , , , , ... is an
1
1
1 __ 1 _ _ _
patterns. Examples of such sets are; the 2 6 18 54
set of natural numbers 1, 2, 3, 4, 5, ... , the infinite sequence.
set of positive even numbers 2, 4, 6, 8, 10, A sequence in which its terms are
12, ... , the set of positive odd numbers increasing in value is called an increasing
1, 3, 5, 7, ... and so on. Given any of sequence. For instance, the sequence 11,
these sets, it is easy to determine the 18, 25, 32, 39, . . . is an example of an

next number from the previous one. For increasing sequence. Mathematics for Secondary Schools
instance, the pattern 1, 2, 4, 7, 11, ... shows A sequence in which its terms are
that the first number is 1 , the second is 2, decreasing in value is called a decreasing
the third is 4, the fourth is 7 and the fifth sequence. For instance; 64, 16, 4, 1, ...
is 11 and so on. The pattern is such that is a decreasing sequence.
the difference between two consecutive
numbers follows the pattern of natural A sequence can be extended if its pattern
is known by examining the relationship
numbers. Hence, the sixth number which between consecutive terms. For instance,
follows after 11 is 16.

Student\s Book Form Three 83

18/09/2025 09:59:18
MATHEMATIC F3 SB.indd 83
MATHEMATIC F3 SB.indd 83 18/09/2025 09:59:18