The document provides information about arithmetic sequences including definitions, formulas, examples, and practice problems. It defines an arithmetic sequence as a sequence where each term is obtained by adding a constant difference to the previous term. The common difference is what distinguishes an arithmetic sequence from others. Formulas taught include the general formula for the nth term and examples are provided to demonstrate finding specific terms. Students are then given practice problems to identify arithmetic sequences, find terms, common differences, and solve word problems involving arithmetic sequences.

1. Objectives:
At the end of the lesson, the student
must be able to:
• define and identify arithmetic
sequence;
• determine the nth term of an
arithmetic sequence.
• Given the first few terms of an
arithmetic sequence, find the
common difference and the nth for
a specified n.

2. Arithmetic Sequence

3. – Consider the situation below.
• A school sets a fine of Php 30 for
the first littering offense. The fine
increases by Php 5 for each
subsequent offense.
• How much will a student be fined
for the second offense? Third
offense? Sixth offense?

4. What is it?
• An arithmetic sequence is a
sequence where every term after
the first is obtained by adding a
constant called the common
difference.
• The sequences 1, 4, 7, 10, ... and
15, 11, 7, 3, ... are examples of
arithmetic sequences since each one
has a common difference of 3 and
4, respectively.

5. General Formula:
An= a1+(n-1)d
a = first term
n = no. of terms
d = common difference
(term-previous term)
An = nth term

6. Points to Ponder
• In order to identify if a
pattern is an arithmetic
sequence you must examine
consecutive terms. If all
consecutive terms have a
common difference you can
conclude that the sequence is
arithmetic.

7. Example
•What is the 10th
term of the
arithmetic sequence
5, 12, 19, 26, ...?

8. Example
1. 2,7,12 find d and
a12
2. 6, 10, 14 find a50
d=4
Find the variables being asked.

9. Find the variables being asked.
1. 2,7,12 find d and a12
d=5
a12=a+(n-1)d
=2+(12-1)5
=2+11(5)
=2+55
answer: 57
2. 6, 10, 14 find a50
d=4
t50=6+(50-1)4
=6+(49)4
=6+196
=202
Examples:

10. Oral Activity
• Which of the following sequences is
an arithmetic sequence? Why?
1. 3, 7, 11, 15, 19.
2. 4, 16, 64, 256
3. 48, 24, 12, 6, 3, ...
4. 1, 4, 9, 16, 25, 36
5. -2, 4, -8, 16, ...

11. Oral Activity
• Find the missing terms in
each arithmetic sequence.
a. 3, 12, 21, __, __, __
b. 8, 3, 2 , __, __
c. 5, 12, __, 26, __
d. 2, __, 20, 29, __
e. __, 4, 10, 16, __

12. • Find the 25th term of
the arithmetic sequence
3, 7, 11, 15, 19,...

13. • The second term of an
arithmetic sequence is
24 and the fifth term is
3.
Find the first term and
the common difference.

14. • How many terms are in
an arithmetic sequence
whose first term is -3,
common difference is 2,
and last term is 23?

15. • Give the arithmetic sequence
of 5 terms if the first term
is 8 and the last term is
100.

16. 1. Find the 9th term of the
arithmetic sequence with first
term of 10 and d= 0.5
2. In the sequence 50, 45,40,35,
… , Which term is 5?
3. Find the 16th term of the
sequence 1, 5, 9, 13, …

17. 3. Find the 15th term of the A.S, if the
fifth term is 12 and the tenth term is -3
t5= a + (5-1)d
t10= a + (10-1)d
(a+4d=12)-1 a+4d=12
a+9d=-3 a+4(-3)=12
-a-4d=-12 a-12=12
a+9d=-3 a=24
5d=-15 t15= a +(15-1)d
d=-3 =24+14(-3)
=14+(-42)
= -15

18. 4. Find the value of k if 6-2k,
3k+1, and 5k form an A.P.
(3k+1)-(6-2k)=(5k)-(3k+1)
3k+1-6-2k=5k-3k-1
5k-5=2k-1
3k=4
k= 4/3

19. 5. Insert three arithmetic
means between 4 and 10
4, t2,t3,t4,10 t2=4+3/2= 5 ½
t5=a +(5-1)d t3=5 ½+3/2=7
10=4+4d t4=7+3/2= 8 ½
6=4d
d=3/2

20. ACTIVITIES

21. Good Luck!!!

22. I. Determine which of the following sequences are
in A.P. For those that are in A.P, give the
common difference, and the next three terms
of the sequence.
1. 0.1, 0.01, 0.001…
2. 40, 42, 44, 46…
3. 5, 8, 11, 14…
4. 1/3, 1/4, 1/6, 1/12…
5. 1.2, 1.8, 2.4…
6. -11, -7, -3, 1…
7. x+2, 2x+1, 3x…
8. 1/3, 1, 5/3..
9. 5/3, 15/4, 5…
10. √2, √3, √4, √5…

23. II. Given the first term (a), and
the common difference (d) of
an A.P, find the next 5 terms.
1. a = 2/5 d = 1/10
2. a = 1.5 d = 0.3
3. a = 3 d = -5
4. a = -3 d = 2
5. a = x+4 d = x-2

24. III. Find the common difference
and insert four arithmetic means
between the given numbers.
1. 9 and 24
2. -25 and 3
3. 4 and 179
4. 50.1 and 50. 7
5. a and a+12
6. x + 2 and x + 10

25. IV. Problem solving. Find the variable
being asked.
1. If 5x – 3, x + 2 and 3x – 11 form an
A.P, find x and t21.
2. If the first term is -4, and the
common difference is 3, what term is
116?
3. The ninth term of an A.P is 15, and
the 17th term is 27, find the a and d.

26. 4. The third term of an A.P is 9 and
its 7th term is 49, what is the 11th
term?
5. A carpenter made a ladder with 16
rungs. The bottom rung is 70 cm.
if each succeeding rung is 1 cm
shorter than the preceding, how
long is the top most rung?

27. Answers

28. Test I answers:
1. Not A.P
2. A.P, d = 2, Next 3 terms = 48, 50, 52
3. A.P, d = 3, Next 3 terms = 17, 20, 23
4. A.P, d = -1/12, Next 3 terms = 0, -
1/12, -1/6
5. A.P, d = 0.6, Next 3 terms = 3, 3.6, 4.2
6. A.P, d = 4, Next 3 terms = 5, 9, 13
7. A.P, d = x-1, Next 3 terms = 4x-1, 5x-
2, 6x-3
8. A.P, d = 2/3, Next 3 terms = 2 1/3, 3, 3
2/3
9. Not A.P
10. Not A.P

29. Test II answers:
1.1/2, 3/5, 7/10, 4/5,
9/10
2.1.8, 2.1, 2.4, 2.7, 3
3.-2, -7, -12, -17, -22
4.-1, 1, 3, 5, 7
5.2x+2, 3x, 4x-2, 5x-4,
6x-6

30. Test III answers:
1. d = 3, Four arithmetic means = 12, 15,
18, 21
2. d = 28/5, Four arithmetic means = -19
2/5, -13 4/5, -8 1/5, -2 3/5
3. d = 35, Four arithmetic means = 39,
74, 109, 144
4. d = 0.12, Four arithmetic means =
50.22, 50.34, 50.46, 50.58
5. d = 12/5, Four arithmetic means = a +
12/5, a + 24/5, a + 36/5, a + 48/5
6. d = 8/5, Four arithmetic means = x +
18/5, x + 26/5, x + 34/5, x + 42/5

31. Test IV answers:
1.x = 3, t21 = -128
2.n = 41st term
3.d = 3/2, a = 3
4.11th term = 89
5.t16 = 55 cm

33. Prepared by:
• Marx Lennin Cabaltican
• Bernadette Aubrey Cabrera
• Precious Fernandez