Question

Each term of a sequence, after the first term, is inversely proportional to the term preceding it, and the constant of proportionality stays the same. If the first term is 2 and the second term is 5, what is the 12th term?

Answer 1

Let k be the constant so a_n = k / a_{n-1}. From a1 = 2 and a2 = 5, k = a1·a2 = 10. Then a3 = 10/5 = 2, a4 = 10/2 = 5, so the sequence alternates 2, 5, 2, 5, ... Thus the 12th term (even index) is 5.