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Week 1 5 Jan - 9 Jan 2009

Arithmetic Sequences

A sequence is a set of numbers in a specific order. What this means is that the set of numbers can be put into a one-to-one correspondence with the Counting Numbers (1, 2, 3, 4, ... ). Thus, you can talk about the 1st element (or term) in a sequence or the 10th element in a sequence or the 101st element in a sequence.


An arithmetic sequence is a sequence in which the difference between any two consecutive terms is the same, i.e., the difference is a constant.

Arithmetic sequences frequently occur in problem solving situations.


Examples

The sequence that begins 1, 4, 7, 10, 13, 16, . . . is an arithmetic sequence since the difference between consecutive terms is always 3.


The sequence that begins 8, 6, 4, 2, 0, -2, -4, . . . is an arithmetic sequence since the difference between consecutive terms is always -2.


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.

Consider the sequence:
4, 11, 18, 25, 32, . . .

Since:

11 - 4 = 7

18 - 11 = 7

25 - 18 = 7

32 - 25 = 7

the sequence is arithmetic. We can continue to find subsequent terms by adding 7. Therefore, the sequence continues:
39, 46, 53, etc.
The Formula for the nth Term in an Arithmetic Sequence

Consider the following table and look for a pattern:


Term 1 4
Term 2 4 + 7 = 4 + (1 X 7) = 11
Term 3 11 + 7 = 4 + 7 + 7 = 4 + (2 X 7) = 18
Term 4 18 + 7 = 4 + 7 + 7 + 7 = 4 + (3 X 7) = 25
.
.

Term 12 4 + (11 X 7) = 81
.
.

Term n = 4 + [(n - 1) X 7]

The same strategy can be used with any arithmetic sequence.

If the first term is designated by the letter a, and the common difference is designated by the letter d,
The nth term of an arithmetic sequence
= a + [(n - 1) X d]
Using The Formula

Use the formula to find the 8th term of the sequence that begins with 11 and has a common difference of 4.

In this example, a = 11 (the first term), d = 4 (the common difference), and n = 8 (the term we are looking for).You can calculate the 8th term using the formula:Term 8 = 11 + [(8 - 1) X 4] = 11 + [7 X 4] = 11 + 28 = 39

Animation 1

Animation 2

PROGRAM DIDIK CEMERLANG AKADEMIK SPM

Organized by

Jabatan Pelajaran Pulau Pinang

Function

Progression

Quadratics Equations

Linear Laws

Quadratics Functions

Integrations

Simultaneous Equations

Trigonometric Functions

Coordinates Geometry

Vector

Indices and Logarithmas

Permutation and Combination
Statistics

Probability

Circular Measure

Probability Distributions

Differentiation

Linear Programming

Solutions of Triangles

Motion along A straight Line

Index Number

Summartive Form 5

Summartive Form 4

Model SPM Paper 1

Model SPM Paper 2

Syllabus And Curriculum Specifications

Additional Mathematics Syllabus
Mathematics Syllabus

Curriculum Specifications Additional Mathematics Form 5
Curriculum Specifications Additional Mathematics Form 4

Curriculum Specifications Mathematics Form 5
Curriculum Specifications Mathematics Form 4
Curriculum Specifications Mathematics Form 3
Curriculum Specifications Mathematics Form 2
Curriculum Specifications Mathematics Form 1

Teaching and learning Calender 2009

Additional Mathematics T&L Calender 2009 Form 5

Additional Mathematics T&L Calender 2009 Form 4

Mathematics T&L Calender 2009 Form 5

Mathematics T&L Calender 2009 Form 4

PERSEDIAN TAHUN 2008

Persedian Tahun 2009 saya mulakan pada 1 dis 2008. Saya akan mengemaskini laman blog yang lama kepada bentuk paparan sekarang. Telah lama saya mengidam mempunyai laman blog sendiri dengan harapan semua bahan yang saya ada akan dapat dikongsi bersama-sama rakan guru yang lain dan seluruh pelajar diseluruh malaysia mahupun seluruh dunia.Semuga laman blog ini akan lebih memberi manafat. Teringat kata-kata Allahyarham Dato Razali Ismail Timbalan Menteri Pelajaran dalam ucaputamanya di Majlis Persidangan Tahunan Jemaah Nazir dan Jaminan Kualiti ke 46 yang sempat saya hadiri.Dato menyatakan bahawa kalau dahalu orang mengatakan "Knowledge is power" sekarang ni ia patut diubah kepada "Knowledge sharing is power".Itulah dakwah terakhir dato agaknya kerana pada jam 10.30 beliau merasmikan persidangan sebelum beliau pergi ke IAB untuk satu majlis yang lain. Masih terdengar-dengar ucapannya agar semua warga pendidikan mencontohi rasullah dalam menyampaikan dakwahnya. Amalkan sifat Siddik, Amanah, Tabliq dan fattanah.Seluruh warga pendidikan memang terasa kehilangan Dato. Alfatihah ...Semuga allah mencucuri rahmat keatas roh Dato.