Observe the following pattern (i)`1^2=1/6[1xx(1+1)xx(2xx1+1)]`, (ii)`1^2+2^2=1/6[2xx(2+1)xx(2xx2+1)]`, `1^2+2^2+3^2=1/6[3xx(3+1)xx(2xx3+1)],` `1^2+2^2+3^2+4^2=1/6[4xx(4+1)xx(2xx4+1)],` and find the values of each of the following `1^2+2^2+3^2+4^2+ddot+10^2,` `5^2+6^2+7^2+8^2+9^2+10^2+11^2+12^2`

Explanation

To solve the problem, we will use the formula for the sum of squares of the first n natural numbers, which is given by:

\[ S_n = \frac{n(n + 1)(2n + 1)}{6} \]

### Step 1: Calculate \(1^2 + 2^2 + 3^2 + \ldots + 10^2\)

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