Solved Examples on Algebraic Pattern

Example 1: 1, 2, 3, 5, 8, 13, _, _

Complete the above sequence of number.

Solution:

We can use addition to figure out the next two numbers in this pattern.

In the example, 1 + 2 = 3 and 2 + 3 = 5, we could say that the rule for this Algebraic pattern is “add the previous two numbers in the pattern together to find the next number.” So, we add 8 + 13 and get 21.

Then, we add 13 + 21 and get 34. Our finished pattern looks like this:

Final Pattern: 1, 2, 3, 5, 8, 13, 21, 34.

Example 2: 4, 8, _, 16, 20, 24, _.

What numbers complete this pattern?

Solution:

To solve this example, from the term 4th, 5th and 6th it is observed that this pattern follows the rule “Add the difference of any two terms to obtain next term”. Here the number which is added to obtain next term is 4.

Hence the third term will be: 8+4=12.

Similarly, the seventh term will be: 24+4=28.

Hence the final pattern will be: 4, 8, 12, 16, 20, 24, 28.

Example 3: 47, 43, 40, 38, 37, 33, _, _.

What numbers complete this pattern?

Solution:

We know we will need to subtract because the numbers get smaller as we read from left to right.

We find the answer by subtracting the number on the left from the number to its right.

The problems in this pattern look like this:

47 – 43 = 4, 43 – 40 = 3, 40 – 38 = 2, 38 – 37 = 1, 37 – 33 = 4.

The subtraction of numbers follows a pattern. The numbers are subtracted as: 4, 3, 2, 1, 4 and so on. So as per this pattern the next differences would be 3, 2, 1 and again 4, 3, 2, 1 and so on.

We are required to obtain the next two numbers, according to this pattern these two numbers will be:

33-3 = 30 and 30-2 = 28.

Hence the final pattern will be: 47, 43, 40, 38, 37, 33, 30, 28.

Algebraic Patterns are sequences of numbers or symbols that follow a specific rule or formula. These patterns can be expressed using algebraic equations or expressions. For example, a simple algebraic pattern might involve adding a fixed number to each term to generate the next term, or multiplying each term by a constant factor.

Algebraic patterns are often used in mathematics to analyze and predict sequences of numbers or to solve problems involving patterns and sequences. They are fundamental in algebraic thinking and are widely used in various fields such as mathematics, computer science, and engineering.