Connected Math Variables and Patterns

Introduction about connected math variables and patterns:

Variables are one of the branches in algebra. In math, variables are very necessary concept. It does not change the meaning of expressions. We are mostly use variables to stand for the algebra expression like a,b,c and d. In math, generally variables can be defined using alphabets. Patterns are generally the collection of numbers which are listed in an order under a certain conditions. There are three different types of general patterns like Arithmetic Pattern, Geometric Pattern and Alphabetic Pattern. Here we are going to study about connected math variable and patterns.

Examples of Connected Math Variables:

Example 1:

(6m^2+9) + (-5m^2+7).

Solution:

Step 1: Here we are going to add the two terms

Step 2:  Its also like a normal addition.

Step 3: It can be written as 6m^2-5m^2+9+7.

Step 4: Now we can easily add the terms.

Step 5: Therefore, the answer is m^2+16.

Example 2:

Add (8n3+12) +( -15n3-6)

Solution:

Step 1: Here we are going to add the two binomials.

Step 2:  Its also like a mathematical addition.

Step 3: It can be written as 8n^3-15n^3+12-6.

Step 4: Now we can easily add the terms.

Step 5: Therefore, the answer is 7n^3+6.

These are the examples of connected math variables. Having problem with trig identities solver keep reading my upcoming posts, i will try to help you.

Examples of Patterns:

Example 1:

Compute the missing terms from the pattern given below.

2, 4, 8, 16, 32, 64, ___, ____

Solution:

Step 1: The first term of the pattern is 2.

Step 2: The second term of the pattern = 2 `xx` 2 = 4.

Step 3: The third term is 4 `xx` 2 = 8.

Step 4: The fourth term is 8 `xx` 2 = 16.

Step 5: Similarly, the missing terms can be determined as follows.

Step 6: The seventh term will be 64 `xx` 2 = 128.

Step 7: The eighth term is 128 `xx` 2 = 256(So, the pattern is we need to multiply 2 with the previous term).

Step 8: Therefore, the pattern is 2, 4, 8, 16, 32, 64, 128 and 256.

Example 2:

Compute the next two terms in the pattern given below.

1, 3, 5, 7, 9, 11, ___, ____

Solution:

Step 1:The first term of the pattern is 1

Step 2:The second term of the pattern = 1 + 2 = 3

Step 3:  The third term is 3 + 2 = 5

Step 4: fourth term is 5 + 2 = 7

Step 5: Similarly, the missing terms can be determined as follows.

Step 6: The seventh term will be 11 + 2 = 13

Step 7: The eighth term is 13 + 2 = 15

Step 8: This is an odd sequence of number.

Step 9: So the exact pattern is 1, 3, 5, 7, 9, 11, 13 and 15.

These are the example problems of connected math variables and patterns.