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

Answer:

The recursive formula to generate the sequence 9.6,-4.8,2.4,-1.2,0.6....

$a_n=-\frac{a_n-1}{2}$

Step-by-step explanation:

Given

f(1)=9.6

The given sequence

9.6,-4.8,2.4,-1.2,0.6....

$a_1=9.6$

$a_2=4.8$

$a_3=2.4$

$\frac{a_2}{a_1} =\frac{-1}{2}$

$a_2=-\frac{a-1}{2}$

similarly , we get

$\frac{a_3}{a_2} =\frac{2.4}{-4.8}$

By simplification we get

$a_3=-\frac{a_2}{2}$

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$a_n=-\frac{a_n-1}{2}$

Hence, the recursive formula for the given sequence

$a_n=-\frac{a_n-1}{2}$.

Answer 2

N-1(-1/2) is the formula because the sequence is taking half of the previous number and changing its sign