Question

Which recursive formula can be used to generate the sequence shown, where f(1) = 9.6 and n > 1?

9.6, –4.8, 2.4, –1.2, 0.6,

Answer 1

The recursive formula to generate the sequence with f(1) = 9.6 and n > 1 is f(n) = -0.5 × f(n-1), reflecting the pattern where each term is half the previous term and alternates in sign.

Step-by-step explanation:

To generate the given sequence where f(1) = 9.6 and for n > 1, we need a recursive formula that reflects the pattern of the sequence.

Observing the sequence, we can see that each term is half of the previous term and alternates in sign.

So, the recursive formula can be stated as:

For n = 1: f(1) = 9.6

For n > 1: f(n) = -0.5 × f(n-1)

This formula indicates that to get the nth term in the sequence, you multiply the (n-1)th term by -0.5.

For instance, to calculate f(3), you would take f(2), which is -4.8, and multiply it by -0.5 to get 2.4.