Page 98 - Mathematics_Form_3

Sequences and series

Example 4.10 (e) 1.3 + 2 + 2.7 + 3.4 + · · ·
17
7 __
___
3 __
1 __
The second term of an arithmetic (f) − − − −
8
4
8
2
progression is 15 and the fifth term is 2. List the first 5 terms of an arithmetic
21. Find the common difference and progression formed by counting in
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the first term. seven starting from 5, and determine
th
Solution the formula for the n term.
Given A = 15 and A = 21 .
2 5 3. The fourth and fifth terms of an
From A = A + (n − 1) d , it gives arithmetic progression are 47 and
n 1
A = A + d = 15 (1) 52, respectively. Find,
2 1
(a) the common difference.
A = A + 4d = 21 (2)
5 1
(b) the first term.
Combine equations (1) and (2) (c) the thirteenth term.
simultaneously as follows.
4. If the first term of an arithmetic
(3)
A + d = 15 progression is 3 and the common
1
(4)
{ A + 4d = 21 difference is 4, find the n term.
th
1
Subtract equation (3) from equation 5. The third term of an arithmetic
(4) to get 3d = 6, from which d = 2. progression is 9 and the common
Substituting d = 2 in equation (3) difference is 2. Find,
gives A = 13. (a) the first term.
1
th
Therefore, the common difference is 2 (b) the 200 term.
th
and the first term is 13. (c) the n term.
6. Find the number of terms in the
following arithmetic series:
Exercise 4.3
(a) 2 − 9 − 20 − 31 − ··· − 130.
1. Which of the following expressions
1 __
1 __
3 __
1 __
(b) 6 + 7 + 8 + ··· + 17 .
are arithmetic progressions? Write 4 2 4 2 Mathematics for Secondary Schools
the common difference for those (c) 407 + 401 + 395 + ··· + 131.
which are arithmetic progressions.
th
1 __
1 __
1 _
(a) + + + 1 7. Find the n term of the arithmetic
4 3 2 progression whose first term is x + 2
(b) 26 + 19 + 12 + 5 − 2 and the common difference is 3.
(c) 2 + 2 . 2 + 2 . 22 + 2 . 222 8. The fourth term of an arithmetic

progression is 11 and the sixth term
(d) − 5 + 4 + 12 + 5 − 2 is 17. Find the tenth term.

Student\s Book Form Three 91

18/09/2025 09:59:21
MATHEMATIC F3 SB.indd 91 18/09/2025 09:59:21
MATHEMATIC F3 SB.indd 91