Hey all. I have a problem in my stage 2 pure maths paper that I'm not sure how to solve. Here it is:
Let x(1), x(2), x(3),... be a sequence of integers defined recursively by :
x(1) = 3, x(2) = 18, and x(n) = 6x(n-1) - 9x(n-2)
for integers n >= 3. Conjecture a formula for x(n) and prove it using mathematical induction.
I'm really not sure how to start it... I think I will be fine with the induction but am not sure how to get the formula...