Question

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Answer 1

• 341

Explanation:

We observe the pattern:

• 1, 5, 13, 25, ..

It can be put as:

• 0 + 1, 1 + 4, 4 + 9, 9 + 16, ..

or

• 0² + 1², 1² + 2², 2² + 3², 3² + 4², ..

The nth term is going to be:

• (n - 1)² + n²

The sum of the 31 terms will be:

• N = 0² + 1² + 1² + 2² + 2² + 3² + 3² + ... + 30² + 30² + 31²

or

• N = 2(1² + 2² + 3² + ... + 30²) + 31²

Use the formula for sum of the first n squares:

• 1² + 2² + 3² + ... + n² = n(n + 1)(2n + 1)/6

The sum N equals:

• N = 2(30*31*61)/6 + 31² = 10*31*61 + 31²

And the value of N/31 is:

• 10*31 + 31 = 341