Page 92 - Mathematics_Form_3

Sequences and series

th
Therefore, the next two terms are 4. If the n term of a sequence is 2n + 1,
− 4 and − 6 . find the tenth term.
th
1
1
(c) In the sequence , , , , . . . 5. If the n term of a sequence is 4n − 1,
1 __ 1 __ ___ ___
3 6 12 24 write the set of the first five terms.
Every term is obtained by multiplying
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1 6. Find the general term of the sequence
the previous term by , so that the
2 1, − 1 , 1, − 1, 1, …
next two denominators are 48 and 7. The n term of a certain sequence is
th
96. 2 n− 1 . Find the sum of the first three
1 ___
Therefore, the next two terms are terms.
48 8. Find the general term of the sequence
1 ___
and .
96 3, 7, 11, 15, 19, . . .
9. Find the next two terms of the
Example 4.5 5 __ 13 19
__
__
sequence , , 4, , . . .
2
4
4
If the n term of a sequence is 3n − 5, 10. The general term of a certain
th
find the third term. 1

sequence is _ n . Find the
Solution 2 + ( − 1)
If the n term is 3n − 5, then the 3 term first four terms. Is the sequence
rd
th
is obtained when n = 3. increasing or decreasing? Give
rd
The 3 term = 3 × 3 − 5 reasons.
= 4
Therefore, the third term is 4. Series
Suppose that your mobile phone data
usage increases by 2 GB per month,
Exercise 4.1
thus, the total usage over time forms a
1. Find the next two terms of each of series. For instance, 2 GB in January,
the following sequences: 4 GB in February, 6 GB in March, and
( a ) , , , . . . so on. The total usage is 2 + 4 + 6 + ...
1 __ 2 __ 3 __
2 3 4
Engage in Activity 4.2 to learn how to
1 __
1 __ 1 __
( b ) 1, − , , − , . . . Mathematics for Secondary Schools
2 4 8 deduce the general pattern of a series.
( c ) 1, 2, 6, 24, 120, . . .
Activity 4.2: Deducing the general
( d ) 1, − 1, 1, − 1, . . . pattern of a series
2. Find the n term of the sequence Individually or in a group perform the
th
2, 5, 8, 11, 14, ... following tasks:
3. Find the n term of the sequence 1. Put matchsticks or toothpicks on
th
3, 6, 9, 12, . . . your desk.

Student\s Book Form Three 85

18/09/2025 09:59:19
MATHEMATIC F3 SB.indd 85
MATHEMATIC F3 SB.indd 85 18/09/2025 09:59:19