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, ...

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betterthanpaul betterthanpaul · Answer 1 · 2016-01-26T17:59:38+01:00

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

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lublana lublana · Answer 2 · 2019-07-01T11:49:06+02:00

Answer:

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

[tex]a_n=-\frac{a_n-1}{2}[/tex]

Step-by-step explanation:

Given

f(1)=9.6

The given sequence

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

[tex]a_1=9.6[/tex]

[tex]a_2=4.8[/tex]

[tex]a_3=2.4[/tex]

[tex]\frac{a_2}{a_1} =\frac{-1}{2}[/tex]

[tex]a_2=-\frac{a-1}{2}[/tex]

similarly , we get

[tex]\frac{a_3}{a_2} =\frac{2.4}{-4.8}[/tex]

By simplification we get

[tex]a_3=-\frac{a_2}{2}[/tex]

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[tex]a_n=-\frac{a_n-1}{2}[/tex]

Hence, the recursive formula for the given sequence

[tex]a_n=-\frac{a_n-1}{2}[/tex].