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

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

Answer 2

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

`a_n=-(a_n-1)/(2)`

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`

`(a_2)/(a_1) =(-1)/(2)`

`a_2=-(a-1)/(2)`

similarly , we get

`(a_3)/(a_2) =(2.4)/(-4.8)`

By simplification we get

`a_3=-(a_2)/(2)`

..................................................

......................................................

`a_n=-(a_n-1)/(2)`

Hence, the recursive formula for the given sequence

`a_n=-(a_n-1)/(2)`.