SPM Form 5 Add Maths_Chapter 01 Progressions

There are generally two types of Progressions which are Arithmetic Progression (AP) and Geometry Progression (GP).

For AP, there are two formulas which one is to find the Nth Term and the other is to find out the Sum of N terms.

"T_n = a +(n-1)d" is used to find the Nth term in a arithmetic series. For example, a series is given as shown below:

1, 3, 5, 7, 9, x, y, z,...........n

a is the first term in the series.

d is the common difference which can be find by subtraction. 

i.e 2nd term - 1st term = 3-1 = 2; 3rd term-2nd term = 5-3 = 2 and so on..

Thus, a = 1, d = 2

Students should be able to find out the value of "x", "y" & "z" immediately by adding the common difference to the number before these terms in the series.

x= 9+2 = 11; y= 11+2 = 13; z = 13+2 = 15

However, if there is a situation that required students to find the 100th term by providing the series above, it is impossible for students to add up in this way up till the 100th term, thus this is the application of the formula where students can easily find the 100th term by doing the below calculation.

T₁₀₀ =1 +(100-1)(2) = 199

"S_n = n/2 [2a+(n-1)d]" applies when students were asked to find the Sum up to nth term. For example, the sum up to 5th term,

Method without applying the formula will be: 1+3+5+7+9 = 25

Method with formula applies: S₅ = 5/2 [2(1)+(5-1)(2)] = 25

The video below shows a more complex example relating to AP and also introducing another formula relate to the 'Last' term.
S_n = n/2 [a+L]

The video below is made to enhance the understanding of students towards the whole concept of AP with the use of Past Year Question as examples.

In AP, we talk about common difference which is basically just subtraction. Now, in GP a new term known as "common ratio" is introduced. When the word "Ratio" is seen, students should now know that it involves dividing. Similar to AP, formulas are developed to find the Nth term and the Sum up to Nth term. What students should bear in mind is that:
To find a common difference: Subtraction involves~ d= 2nd term - 1st term
To find a common ratio: Division involves~ r= 2nd term/ 1st term

Infinite Sum is one of the topic include in GP which means if "n" approaches infinity, what will be the Sum?

The videos below are using Past Year Question as further examples to enhance students' understanding.

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