If the 2nd term of a geometric progression is 6 and the 5th term is 162, find the common ratio.

Let the first term be a and common ratio r. Then ar = 6 and ar^4 = 162. Dividing: r^3 = 162/6 = 27, so r = 3. The first term is then a = 6/3 = 2. Option A (2) is the value of the first term mistaken for the ratio, and option D (6) is the value of the 2nd term.