Three consecutive terms of an AP have a given sum and product. Find the terms.

1. 1 · Write what is given and what is to be found. Write the sum and the product, and 'To find: the three terms'.
2. 2 · Write the formula or theorem. Take the terms as a − d, a, a + d, so that d cancels in the sum.
3. 3 · Use the sum. (a − d) + a + (a + d) = 3a. Solve for a.
4. 4 · Use the product. (a − d) × a × (a + d) = a(a² − d²). Substitute a and solve for d².
5. 5 · Write the terms. Use d and −d; both give the same three numbers in reverse order.
6. 6 · Check and box the answer. Add and multiply your three numbers to check them against the data.

Scoring tip: Choosing a − d, a, a + d saves time, because the sum gives a at once.