Page 91 - Mathematics_Form_3

Sequences and series

in the sequence 1, 2, 3, 4, ..., the next Example 4.3
term is 5 since each term increases by Given the sequence 2, 4, 6, 8, . . . , find:
1. In the sequence 2, 1, 4, 3, 6, 5, ..., the (a) the fifth term.
pattern alternates between subtracting (b) the n term.
th
1 and adding 3, so the next two terms
FOR ONLINE READING ONLY
are 8 and 7. Solution
(a) The difference between two
consecutive terms is 2. Hence,
Example 4.1 every term is obtained by adding
2 to the previous term. Thus, the
List down the terms of each sequence
th
5 term = 8 + 2 = 10.
obtained from the following descriptions. Therefore the fifth term is 10.
st
(a) Multiples of 3 which lie between (b) The 1 term is 2 = 2 × 1
nd
0 and 20. The 2 term is 4 = 2 × 2
rd
(b) Squares of counting numbers from The 3 term is 6 = 2 × 3
th
1 to 10. The 4 term is 8 = 2 × 4
(c) Counting numbers less than 50 but ⋮ ⋮
th
divisible by 9. The n term = 2 × n
th
Solution Therefore, the n term is 2 × n or 2n.
(a) The terms are 3, 6, 9, 12, 15, 18.
(b) The terms are 1, 4, 9, 16, 25, 36, Example 4.4

49, 64, 81, 100 . Find the next two terms in each of the
(c) The terms are 9, 18, 27, 36, 45. following sequences:
(a) 22, 37, 52, 67, . . .
Mathematics for Secondary Schools Find the fifth term of the sequence Solution
(b) 4, 2, 0, − 2, . . .
Example 4.2
1
1
1 __ 1 __ ___ ___
(c) , , , , . . .
3 6 12 24
1, 4, 7, 10, . . .
(a) In the sequence 22, 37, 52, 67, ...,
every two consecutive terms differ
Solution
by 15. Thus, the fifth term is
From the given terms of the sequence,
67 + 15 = 82, and the sixth term is
the difference between two consecutive
terms is 3. Hence, every term is obtained
Therefore, the next two terms are
by adding 3 to the previous term. Thus,
82 and 97.
the fifth term is 10 + 3 = 13. Therefore, 82 + 15 = 97.
the fifth term is 13. (b) In the sequence 4, 2, 0, − 2, ... every
two consecutive terms differ by − 2.

84 Student\s Book Form Three

18/09/2025 09:59:18
MATHEMATIC F3 SB.indd 84 18/09/2025 09:59:18
MATHEMATIC F3 SB.indd 84