ARITHMETIC SERIES

Examine the following sequence:

3,6,12,24,48,96,…

1,1,2,3,5,8,13,21,…

Examine the following sequence:

3,6,12,24,48,96,…

The succeeding term is two times the previous term.

For example the 2nd term: 6 = 3G2

Examine the following sequence:

The succeeding term is the sum of the two previous term.

For example the 6th term is: 8 = 5+3

1,1,2,3,5,8,13,21,…

ARITHMETIC SERIES

“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.

WATER CHARGE MATRIXWater

Consumption (cu. meters)

Charge in Pesos

10 or less 150

11

12

13

14

15

WATER CHARGE MATRIXWater

Consumption (cu. meters)

Charge in Pesos

10 or less 150

11 170

12

13

14

15

WATER CHARGE MATRIXWater

Consumption (cu. meters)

Charge in Pesos

10 or less 150

11 170

12 190

13

14

15

WATER CHARGE MATRIXWater

Consumption (cu. meters)

Charge in Pesos

10 or less 150

11 170

12 190

13 210

14

15

WATER CHARGE MATRIXWater

Consumption (cu. meters)

Charge in Pesos

10 or less 150

11 170

12 190

13 210

14 230

15

WATER CHARGE MATRIXWater

Consumption (cu. meters)

Charge in Pesos

10 or less 150

11 170

12 190

13 210

14 230

15 250

Study the following sequence.

1, 2, 3, 4, 5,…

0, 5, 10, 15, 20, 25,…5, 2, -1, -4, -7, -10,…

•The terms are obtain by adding 1 to each succeeding terms.

1, 2, 3, 4, 5,…

•The terms are obtain by adding 5 to each

succeeding terms.

0, 5, 10, 15, 20, 25,…

•The terms are obtain by adding –3 to each succeeding terms.

5, 2, -1, -4, -7, -10,…

or example the 2nd term: 2 = 5+ (-3)

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.

•The terms are obtain by adding 1 to each succeeding terms.

1, 2, 3, 4, 5,…

The common difference is

d = 1

•The terms are obtain by adding 5 to each

succeeding terms.

0, 5, 10, 15, 20, 25,…

The common difference is

d = 5

•The terms are obtain by adding –3 to each succeeding terms.

5, 2, -1, -4, -7, -10,…

The common difference is d = -3

The nth term of an arithmetic sequence:

The common difference, d , of an arithmetic sequence:

Illustrative Problem 1: Complete the arithmetic sequence, , up to 8 terms. Solution: Let , , .

Then the common difference is

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

The first 8 terms of the sequence are…

Illustrative Problem 2:

Find the 25th term of the arithmetic series 2, 5, 8, 11, …

Illustrative Problem 3:

Find the arithmetic series of 6 terms if the first term is 27 and the last term is 12.

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?

ARITHMETIC SERIES