Question

The fifth term of a geometric sequence is 781.25. Each term of the sequence is mc019-1.jpg of the value of the following term. Which recursive formula represents the situation?
mc019-2.jpg
mc019-3.jpg
mc019-4.jpg
mc019-5.jpg

Answer 1

Each term is (4/5) of the following term, so a_{n+1} = (5/4)a_n. With a_5 = 781.25, a_1 = a_5*(4/5)^4 = 781.25*(256/625) = 320.

Recursive formula: a_1 = 320, a_n = (5/4) a_{n-1} for n ≥ 2.