Page 97 - Mathematics_Form_3

Sequences and series

In general, if d is the common difference Solution
between two successive terms of an (a) It is an arithmetic series with a
arithmetic progression, use the same common difference, d = .
1 _
procedure to generate the n term as 2
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follows: (b) It is not an arithmetic series since it
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does not have a common difference.
n = 1 ; A = A

1
1
(c) It is an arithmetic series with a
n = 2 ; A = A + d common difference, d = − 2.

1
2
n = 3 ; A = A + d = ( A + d ) + d (d) It is an arithmetic series with a

1
3
2
= A + 2 d common difference, d = − 3.
1
n = 4 ; A = A + d = ( A + 2d ) + d (e) It is not an arithmetic series because

1
3
4
= A + 3 d it has no common difference.
1
n = 5 ; A = A + d = ( A + 3d ) + d (f) It is not an arithmetic series as it

4
5
1
= A + 4 d does not have a common difference.
1
n = 6 ; A = A + d = ( A + 4d ) + d

5
1
6
Example 4.9
= A + 5 d
1
The n term A is obtained by adding A The first term of an arithmetic
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n 1
to the product of ( n − 1 ) and the common progression is 6 and the common
difference d . difference is 5. Find:
Therefore, the n term is given by: (a) the third term.
th
th
A = A + (n − 1 ) d. (b) the n term.

n 1 (a) Given A = 6, d = 5 , n = 3.
Mathematics for Secondary Schools ( a ) 1 + + 2 + A = 6 + (3 − 1 ) ×5
Solution
Example 4.8
1
Identify the arithmetic series from the
From A = A + (n − 1 ) d ,
1
n
following expressions and write down
its common difference:
3
= 6 + 10

3 __
5 __
2
2
= 16 .

( b ) 2 + 4 + 8 + 16
Therefore, the third term is 16.
( c ) 10 + 8 + 6 + 4 + 2
( d ) − 2 − 5 − 8 − 11 (b) A = A + (n − 1 ) d = 6 + (n − 1 ) × 5
1
n
2
( e ) 1 + 2 + 3 + 4 = 5n + 1
2
2
2
(f) 1 − 3 + 5 − 7 + 9 Therefore, the n term is 5n + 1.
th
90 Student\s Book Form Three
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MATHEMATIC F3 SB.indd 90 18/09/2025 09:59:21
MATHEMATIC F3 SB.indd 90