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3 years ago

Which recursive formula can be used to generate the sequence below, where f(1) = 6 and n ≥ 1?

Mathematics

2 answers:

NNADVOKAT [17]3 years ago

7 0

Answer: The correct option is

(B) $f(n+1)=f(n)-5.$

Step-by-step explanation: We are given to select the correct recursive formula that can be used to generate the following sequence :

$f(1)=6,n\geq1,\\\\6,1,-4,-9,-14,...$

Let f(n) denote the nth term of the given sequence. Then, we note that

$f(1)=6,\\\\f(2)=1=6-5=f(1)-5,\\\\f(3)=-4=1-5=f(2)-5,\\\\f(4)=-9=-4-5=f(3)-5,\\\\f(5)=-14=-9-5=f(4)-5,\cdots$

Therefore, the recursive formula can be written as :

$f(n+1)=f(n)-5.$

Thus, the required recursive formula is $f(n+1)=f(n)-5.$

Option (B) is CORRECT.

Nat2105 [25]3 years ago

4 0

Answer:

Step-by-step explanation:

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