Which recursive formula can be used to generate the sequence below, where f(1) = 6 and n ≥ 1? 6, 1, –4, –9, –14, … f (n + 1) = f(n) + 5 f (n + 1) = f(n) – 5 f (n) = f(n + 1 ) – …

Question

asked Jan 20, 2020 79.3k views

2 Answers

Tawnos · Answer 1 · 2020-01-23T18:28:21+0000

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.