The document discusses two arithmetic sequences: 1) 3,6,12,24,48,96,... where each term is double the previous term. 2) 1,1,2,3,5,8,13,21,... where each term is the sum of the two previous terms. It provides examples of how to determine the pattern/common difference that defines an arithmetic sequence and calculates subsequent terms.

1. ARITHMETIC
SERIES

2. Examine the following sequence:
3,6,12,24,48,96,…
1,1,2,3,5,8,13,21,…

3. Examine the following sequence:
3,6,12,24,48,96,…
The succeeding term is two times
the previous term.
For example the 2ndterm:
6 = 3G2

4. Examine the following sequence:
1,1,2,3,5,8,13,21,…
The succeeding term is the sum
of the two previous term.
For example the 6th
term is:
8 = 5+3

5. ARITHMETIC
SERIES

6. “The GSC Water District will impose a new
minimum charge of P150 for first 10 cubic
meters and additional charge of P20 for
every cubic meter in excess of the
minimum effective June 2011…”
Read the information above and complete the
charge matrix below if you want to know how
much will be charged on your water bill.

7. WATER CHARGE MATRIX
Water
Consumption Charge in Pesos
(cu. meters)
10 or less 150
11
12
13
14
15

8. WATER CHARGE MATRIX
Water
Consumption Charge in Pesos
(cu. meters)
10 or less 150
11 170
12
13
14
15

9. WATER CHARGE MATRIX
Water
Consumption Charge in Pesos
(cu. meters)
10 or less 150
11 170
12 190
13
14
15

10. WATER CHARGE MATRIX
Water
Consumption Charge in Pesos
(cu. meters)
10 or less 150
11 170
12 190
13 210
14
15

11. WATER CHARGE MATRIX
Water
Consumption Charge in Pesos
(cu. meters)
10 or less 150
11 170
12 190
13 210
14 230
15

12. WATER CHARGE MATRIX
Water
Consumption Charge in Pesos
(cu. meters)
10 or less 150
11 170
12 190
13 210
14 230
15 250

13. Study the following sequence.
1, 2, 3, 4, 5,…
0, 5, 10, 15, 20, 25,…
5, 2, -1, -4, -7, -10,…

14. 1, 2, 3, 4, 5,…
•The terms are obtain by
adding 1 to each
succeeding terms.

15. 0, 5, 10, 15, 20, 25,…
•The terms are obtain by
adding 5 to each
succeeding terms.

16. 5, 2, -1, -4, -7, -10,…
•The terms are obtain by
adding –3 to each
succeeding terms.
or example the2nd term:
2 = 5+ (-3)

17. Definition: Arithmetic Sequence
An arithmetic sequence is a
sequence in which each term after the
first is obtained by adding the same
fixed number, called the common
difference, to the preceding term.

18. 1, 2, 3, 4, 5,…
•The terms are obtain by
adding 1 to each
succeeding terms.
The common difference is
d=1

19. 0, 5, 10, 15, 20, 25,…
•The terms are obtain by
adding 5 to each
succeeding terms.
The common difference is
d=5

20. 5, 2, -1, -4, -7, -10,…
•The terms are obtain by
adding –3 to each
succeeding terms.
The common difference is
d = -3

21. The common difference, d , of an arithmetic sequence:
The nth term of an arithmetic sequence:

22. Illustrative Problem 1:
Complete the arithmetic
sequence, , up to 8 terms.
Solution: Let , , .
Then the common difference is

23. The first 8 terms of the sequence, using
, are…
The first 8 terms of the sequence are…

24. Illustrative Problem 2:
Find the 25th
term of the
arithmetic series
2, 5, 8, 11, …

25. Illustrative Problem 3:
Find the arithmetic
series of 6 terms if the
first term is 27 and the
last term is 12.

26. Assignment: Solve the following problems
1. What are the first three terms of the arithmetic
series whose 9th term is 16 and 40th term is 47?
2. The 18th and 52nd terms of an arithmetic series
are 3 and 173, respectively. Find the 25th term.
3. Find the sum of all odd integers from 27 to 495,
inclusive.
4. What is the value of k such that ,
, and forms an arithmetic
series?

27. ARITHMETIC
SERIES