Find the value of a sum of squares or cubes that does not start at 1, such as 11² + 12² + ... + 20².

1. 1 · Write what is given and what is to be found. Write the series and note its first and last terms.
2. 2 · Write the formula or theorem. 1² + 2² + ... + n² = n(n + 1)(2n + 1)/6.
3. 3 · Split the sum. (1² + ... + 20²) − (1² + ... + 10²).
4. 4 · Find the larger sum. n = 20: 20 × 21 × 41/6 = 2870.
5. 5 · Find the smaller sum. n = 10: 10 × 11 × 21/6 = 385.
6. 6 · Check and box the answer. Subtract: 2870 − 385 = 2485, and box it.

Scoring tip: Subtract the sum up to the term just before the first term: for 11² onwards, subtract up to 10², not up to 11².