Question

Suppose g1 = 3 and g2 = 5. The rest of the terms in a recursive sequence are given by the formula gn = n·gn-1 + gn-2.

Find the 7th term of the sequence, g7.

Answer 1

We can use the recursive formula to find the values of the sequence:

g3 = 3·g2 + g1 = 3·5 + 3 = 18

g4 = 4·g3 + g2 = 4·18 + 5 = 77

g5 = 5·g4 + g3 = 5·77 + 18 = 395

g6 = 6·g5 + g4 = 6·395 + 77 = 2457

g7 = 7·g6 + g5 = 7·2457 + 395 = 17276

Therefore, the 7th term of the sequence is g7 = 17276.