Which recursive formula can be used to generate the sequence shown, where f of 1 is equal to 9 point 6 and n is greater than or equal to 1 ? 9 point 6 comma negative 4 point 8 comma 2 point 4 comma negative 1 point 2 comma 0 point 6 comma dots
Answer
A
f of n plus 1 is equal to 0 point 5 times f of n
B
f of n plus 1 is equal to f of negative 0 point 5 n
C
f of n plus 1 is equal to f of 0 point 5 n
D
f of n plus 1 is equal to negative 0 point 5 times f of n
Explanation
A recursive rule multiplies each term by the same number to get the next term. Here, −4.8 ÷ 9.6 = −0.5, and the same ratio gives 2.4 from −4.8 and −1.2 from 2.4. Therefore, the rule is f(n + 1) = −0.5 × f(n), which is choice D.
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