#### Question

Using the given pattern, find the missing numbers.

1^{2} + 2^{2} + 2^{2} = 3^{2}

2^{2} + 3^{2} + 6^{2} = 7^{2}

3^{2} + 4^{2} + 12^{2} = 13^{2}

4^{2} + 5^{2} + _ ^{2} = 21^{2}

5^{2} + _ ^{2} + 30^{2} = 31^{2}

6^{2} + 7^{2} + _ ^{2} = __^{2}

#### Solution

From the given pattern, it can be observed that,

1) The third number is the product of the first two numbers.

2) The fourth number can be obtained by adding 1 to the third number.

Thus, the missing numbers in the pattern will be as follows.

4^{2} + 5^{2} + 20^{2} = 21^{2}

5^{2} + 6^{2} + 30^{2} = 31^{2}

6^{2} + 7^{2} + 42^{2} = 43^{2}

Is there an error in this question or solution?

Solution Using the Given Pattern, Find the Missing Numbers. 1square2 + 2square2 + 2square2 = 3square2 , 2square2 + 3square2 + 6square2 = 7square2 , 3square2 + 4square2 + 12square2 = 13square2 Concept: Some More Interesting Patterns.