The document discusses sequences, specifically arithmetic and geometric sequences. It defines an arithmetic sequence as a sequence where each term is found by adding or subtracting the same number to the previous term, called the common difference. A geometric sequence is defined as a sequence where each term is found by multiplying or dividing the previous term by the same number, called the common ratio. It provides formulas for calculating the nth term and sum of the first n terms of arithmetic and geometric sequences. Examples are given of identifying sequences as arithmetic or geometric and calculating terms within sequences.

1. CHAPTER 1
SEQUENCES
- Arithmetic Sequences
- Geometric Sequences

2. Learning
Objectives
 explain the terms sequences, arithmetic and geometric
sequence.
 identify arithmetic and geometric sequence.
 calculate the terms in arithmetic and geometric
sequence.
 calculate the sum of terms in arithmetic and geometric
sequence.
 apply the concepts of arithmetic and geometric
sequences to some common problem in daily life.

3. Arithmetic sequence
 Hot fm. Is having a contest:
 RM 150 for 1st day.
 Increases RM 50 per day
 List the value of the price from 1st to 5th day?
 What is the value of money that the winner on the 5th
day will get?

4. SEQUENCE
• sequence : List of numbers arranged in a specified order.
T1, T2 , T3 , …,
• series is the indicated sum of the terms of the sequence.
T1+ T2 + T3 + …,

5. What is an arithmetic
sequence?
A sequence in which each
term is found by ADDING
or SUBTRACTING the
same number to the
previous term.
4, 8, 12 , 16, 20… 20, 16, 12 , 8 , 4…
-4+4+4 +4 -4 -4-4
T1
+4
T2 T3 T4

6. What is the common
difference?
The difference between each
number. (take 2 terms next to each
other)
4, 8, 12, 16, 20…………..
* 4 is the common difference

7. • 4, 8, 12, 16, 20…………..
T1 T2 T3 T4
Common difference, d = T2-T1
= 8-4
=4
or
Common difference, d = T3-T2
= 12-8
=4

8. Nth term of an arithmetic sequence
d)1n(aT 1n 
nth term
1st term
# of term
that
we are
trying
to find
Common
difference

9. Find the next four terms of each
arithmetic sequence.
1) 26, 21 , 16, … 2) 2 , 10,
18,…

10. TUTORIAL
1)Find the next four terms of each arithmetic sequence.
(a) the 12th term for the sequence 12,15,18,21,…
(b) the 21th term for the sequence 10,25, 40,55,…
(c) the 9th tern for the sequence 8.2,8.4,8.6,8.8,…
(d) the 16th term for the sequence 41, 37,33,29,…
2) What is the number of terms for the following arithmetic sequence?
(a) 55, 60, 65,…,200
(b) 50,62,74,…,614
(c) -5,-4.5,-4,…,1
(d) 300, 293,286,…,62

11. Complete each statement.
170 is the ____th term of –4, 2, 8
 Find the 10th term of the following arithmetic sequence:
2,10,18,…
d)1n(aT 1n 

12. sum of first n terms of an
arithmetic sequence
 d)1n(a2
2
n
Sn 
Sum of the
first nth terms
Number of terms
First Term Common
difference

13. Find the sum of the 1st 50 positive even
integers.

14. What is a geometric sequence?
A sequence in which
each term can be found
by multiplying or dividing
the previous term by the
same number.
3, 9, 27 , 81, 243…………..
x3 x3x3 x3

15. What is the common ratio?
The ratio between 2
successive terms
2, 8, 32, 128, 512…………..

16.  2, 8, 32, 128, 512………….. …………..
T1 T2 T3 T4
Common ratio , r = T2÷T1
= 8÷2
=4
or
Common ratio, r = T3÷T2
= 32÷8
=4

17. Let’s Practice!

18. Is this an arithmetic or geometric
sequence?
10, 15, 20, 25, 30……

19. Is this an arithmetic or geometric
sequence?
2, 12, 72, 432, 2,592……

20. What is the next term in this sequence?
5, -1, -7 -13 , _____

21. What is the next term in this sequence?
-400,-380,-360,-340 , ____

22. What is the next term in this sequence?
12, -48, 192 , -768____

23. Nth term of a geometric sequence
nth term
1st term
# of term
that
we are
trying
to find
Common
ratio
1n
n arT 


24. 1) Find the given term for the following geometric sequences.
(a) The 8th term for the sequence 2,8,32,…
(b) The 9th term for the sequence 6,18,54,162,…
(c) the 12th term for the sequence 1,-2,4,…
(d) The 6th term for the sequence ½, ¼, 1/8, …
2) What is the number of terms for the following
geometric sequence?
a) 10,20,40,…,10240
b) 100,80,64,…,40.96
c) 4,16,64,…,65536
d) 1/81, 1/27,1/9,…3

25. Sum of first n terms of a geometric
sequence
Sum of the
first nth terms
Number of
termsFirst Term
Common
ratio
1rif
1r
)1r(a
S
n
n 


 1rif
r1
)r1(a
S
n
n 


OR

28. 1) All the terms of a geometric sequence are positive.
The third term of the sequence is 45 while the fifth
term is 101.25.Find
(a) the first term and the common ratio.
(b) the sum of the first 5th terms.
2)For a geometric sequence, the second term is 6 and
the sixth term is 7,776. Given that all the terms are
positives, find
(a) the 10th term and
(b) the 15th term.

29. Q&A