Answer:
Step-by-step explanation:
We observe the pattern:
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:
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:
