Quite a number of students failed to understand the easiest way in solving this topic that is also known as sequence of numbers. This type of question normally appear on the Maths Paper 1 ranging from Standard 3 up to Standard 6 and frequently reappear in PMR paper as well but with a new set of numbers that may include advanced topics such as numbers in fraction, decimals, power, roots of a numbers and many more.

Though the set may change, the approach, however shall remain the same. Today’s article will look into some easy approach that will help students in understanding this topic and able to solve the problems in the simplest form.

**STEPS OF SOLUTION**

1. Find the difference of the set of sequence numbers, please take note that the difference could only be obtained between 2 known sequence numbers. Only use **subtraction** or **division** method to find the difference. Kindly refer to the examples below.

2. Identify the type of sequence….ascending of descending? In the case of ascending number, the order of sequence shall be **(+) THE DIFFERENCE or (x) THE DIFFERENCE ( when the difference is 1 or more )**; **in the case of descending number, the order shall be (-) THE DIFFERENCE or (x) THE DIFFERENCE ( when the difference is less than 1)**

3. Work out your calculation from one known number to another by applying the steps mentioned in 2. Compare your answer with the known numbers given. If the numbers are the same, then your DIFFERENCE is correct. But if it is not, then apply the other calculation; (x) THE DIFFERENCE. Once you have completed your set, then move to steps 4.

4. Fill in the empty slots or the unknown numbers by applying the steps mentioned in 1. Take note that the movement of operation may changed once the flow move from different side.

In the case of ascending sequence number with a difference of 2, calculation movement from left to right will have a + or x DIFFERENCE factor; while calculation movement from right to left will have a – or ÷ DIFFERENCE factor. The same applies to the descending sequence number

Now study the example given below

**SAMPLE 1**

Find the value of P, Q and R

**SOLUTION**

The sequence numbers is on ascending order; thus has + or x DIFFERENCE

Since 18 & 21 are 2 known sequence numbers, the DIFFERENCE shall be 21 – 18 = + 3 (order of left to right)

Now apply + 3 from one known number to another and in this case will be : 12 + 3 = 15; 15 + 3 = 18; 18 + 3 = 21; 21 + 3 = 24; 24 + 3 = 27; 27 + 3 = 30

By comparing our results with the given known sequence numbers, it proves our steps are accurate and the answer for **P = 15; Q = 24; R = 27**

**SAMPLE 2**

Find the value of P – Q + R

**SOLUTION**

Descending sequence number, so the difference of 47 – 42 shall be known as – 5 (order of left to right)

47 – 5 = 42; 42 – 5 = 37 (P); 37 – 5 = 32; 32 – 5 = 27; 27 – 5 = 22(Q); 22 – 5 = 17(R)

Since the comparison for the known number suit our calculation, therefore **P – Q + R shall be 37 – 22 + 17 = 32**

**SAMPLE 3**

Find P + Q + R

**SOLUTION**

Descending sequence number, so the difference of 65 – 61 shall be known as – 4 (order of left to right)

81 + 4 = 85(P); 81 – 4 = 77(Q); 77 – 4 = 73; 73 – 4 = 69(R); 69 – 4 = 65; 65 – 4 = 61

Since the comparison of the known number suit our calculation, therefore **P + Q + R = 85 + 77 + 69 = 231**

**SAMPLE 4**

Find P, Q and R

**SOLUTION**

Descending sequence number and since the changes in the fraction involves the the denominator, the the difference has to be less than 1: 3/8 ÷ 3/16 = 3/8 x 16/3 = 1/2 and as such shall be known as (x) 1/2 (order of left to right)

3/2 x 1/2 = 3/4(P); 3/4 x 1/2 = 3/8; 3/8 x 1/2 = 3/16; 3/16 x 1/2 = 3/32(Q); 3/32 x 1/2 = 3/64(R); 3/64 x 1/2 = 3/128

Since the comparison of the known number suit our calculation, therefore **P = 3/4, Q = 3/32 and R = 3/64**

**SAMPLE 5**

Find P + Q + R

**SOLUTION**

Ascending sequence number. Since we aren’t too sure about the changes in the sequence, then let us find and try (+) and (x) differences. (+) differences will gives an answer of + 28.8 ( 57.6 – 28.8) while the (x) differences will give an answer of (x) 2 (57.86 ÷ 28.8).

The sequence for both differences shall read as follows:

1.8 + 28.8 = 30.6; 30.6 + 28.9 = 59.5; 59.5 + 28.8 = 88.3…..obviously our calculation doesn’t suit the sequence order given

1.8 x 2 = 3.6; 3.6 x 2 = 7.2; 7.2 x 2 = 14.4; 14.4 x 2 = 28.8; 28.8 x 2 = 57.6 which seems to suit the given sequence. Therefore, (x) 2 as our difference works. Now let us find P; 1.8 ÷ 2 = 0.9 which is also and answer for P ( working opposite order means opposite operation >>> refer to STEP 4)

Then **P + Q + R = 0.9 + 3.6 + 14.4 = 18.9**