Question

Find a recursive rule for the sequence 1, 4, 9, 22, …

Answer 1

It looks like it's the sum of the previous 2 terms plus the second term

Answer 2

I'm not sure if that's a proper way of defining it.\[a_1 = 1, a_2=4\]
\[a_k =a_{k-1} + a_{k-1} +a_{k-1} =a_{k-1} + 2a_{k-1}\]