The product and sum of three consecutive terms of a GP are given. Find the terms.

How to lay out the answer. Follow the frame, then write it in your own words.

1 · Write what is given and what is to be found. Write the product and the sum, and 'To find: the three terms'.
2 · Write the formula or theorem. Take the terms as a/r, a, ar, so that r cancels in the product.
3 · Use the product. (a/r) × a × ar = a³. Take the cube root to get a.
4 · Use the sum. a/r + a + ar = the given sum. Multiply through by r to get a quadratic in r.
5 · Solve the quadratic. Factorise, e.g. 6r² − 13r + 6 = (2r − 3)(3r − 2) = 0, so r = 3/2 or 2/3.
6 · Check and box the answer. Both values of r give the same terms in reverse order. Check the sum and product.

Scoring tip: Clear the fraction by multiplying by r before you factorise, and write both values of r.