Question

Which recursive formula can be used to generate the sequence below, where f(1) = 3 and n ≥ 1? 3, –6, 12, –24, 48, … f (n + 1) = –3 f(n ) f (n + 1) = 3 f(n ) f (n + 1) = –2 f(n ) f (n + 1) = 2 f(n)

Answer 1

Which recursive formula can be used to generate the sequence below, where f(1) = 3 and n ≥ 1?

3, –6, 12, –24, 48

The recursive formula for this sequence is

f (n + 1) = –2 f(n)

at n=1 f(n)= 3

at n = 2

f(2) = -2 (3) = -6

n = 3

f(3) = -2 (-6) = 12 and so on

Answer 2

The recursive formula for the sequence is:
f(n+1) = -2f(n)

Let's take an example:
Let f(n) = 12 and we need to calculate f(n+1) which should be -24
If we apply the formula than the answer is:
f(n+1) = -2*12 = -24.

I hope that this is the answer that you were looking for and it has helped you.