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A recursive rule is one which can be applied over and over again to its own output
Each number is -4 times the previous one. That means that you can write a recursive rule as: f(1) = -3 f(n) = -4 * f(n-1) The explicit rule involves powers of -4; you can write it as: f(n) = -3 * (-4)^(n-1)
It is often possible to find an explicit formula that gives the same answer as a given recursive formula - and vice versa. I don't think you can always find an explicit formula that gives the same answer.
x1=0 x2=1 for i > 2, xi= xi-1 + xi-2
The term recursive refers to the recurrence or repetition.