can you solve this brilliant math pattern puzzle ?

Math Puzzles or Questions are used to test IQ. Every entrance test includes maths questions and hence it is important to practice. Maths puzzles are equally important in interviews. Here is an interesting math puzzle, try to solve this and share your answer in the comment section.

Missing numbers are the numbers that got missed in the given series of numbers with similar differences among them. The process of writing the missing numbers is termed as finding similar changes between those numbers and filling their missing values in their specific series and places. 

Can You Solve This Brilliant Math Pattern Puzzle? 
If 2=6, 3=12, 4=20, 5=30 and 6=42, what does 9 equal ?

Solution 

This question is basically the application of patterns and sequences. These types of questions can be easily solved if one tries to observe the pattern being followed...

If we observe the pattern carefully ... In each set, the integer before the equal sign is multiplied by its consecutive next integer greater than it, and the result is on the other side of the equal sign.

If the LHS is represented as "A" then RHS can be calculated using the expression => A*(A+1)

for example, in the first set, the integer before the equal sign is 2 which is multiplied by its consecutive next integer greater than it which is 3, and the result is 6 which is on the other side of the equal sign.

in the second set, the integer before the equal sign is 3 which is multiplied by its consecutive next integer greater than it which is 4, and the result is 12 which is on the other side of the equal sign.

applying this pattern, the series looks like

2 = 6 → 2 x 3 = 6

3 = 12 → 3 x 4 = 12

4 = 20 → 4 x 5 = 20

5 = 30 → 5 x 6 = 30

6 = 42 → 6 x 7 = 42

therefore:

7 = 56 → 7 x 8 = 56

8 = 72 → 8 x 9 = 72

9 = 90 → 9 x 10 = 90 is the final solution.

observing the pattern the answer is 90.

There are multiple patterns that satisfy the pattern, I will explain one another pattern.

Here, the first number is what we are given and the second number is what is hidden. Here by taking a close look we will see that the pattern is decoded as

RHS = x+x^2

where x is the number in the LHS

So, by applying this pattern we can actually see the things happening...

for example, in the first set, the integer before the equal sign is 2 hence x is 2, after applying the value in pattern RHS is 2+2^2 = 6

2 + 2^2 = 2 + 4 =6

Similarly in the second set 

the integer before the equal sign is 3 hence x is 3, after applying the value in pattern RHS is 3+3^2 is 12

3 + 3^2 = 3 + 9 =12

applying the same pattern to 9, the solution is 9+9^2 which results in 90 → 9 +9^2 = 9 + 81 =90

The answer could have been different if we take the pattern alternatively. do share your answer in the comment sections if you found a different pattern that satisfies here.