Chegg the fibonacci sequence is defined as fn = fn−2 + fn−1, f1 = 1, f2 = 1. let’s consider another sequence defined recursively also. let j1 = 1, j2 = 1 and for all n ≥ 3, jn = jn−1 + 2jn−2. (a) prove for all n ≥ 1, fn ≥ 3 2 n−2 (b) prove by induction that f3i(every third fibonacci number, f3, f6, f9, . .) is even for i ≥ 1. (c) prove using induction that for any n ≥ 1, jn = 2 n−(−1)n 3 . (d) suppose we are given a 2-by-n grid that we must tile with 1-by-2 dominoes or 2-by-2 squares. prove using induction on n that for any n ≥ 1 the number of different ways to tile the 2-by-n grid is jn+1 where jn+1 is the n + 1-st term in the sequence defined above.