Answer:
Option 4 is correct.
Step-by-step explanation
Here the first term is 8 so  the first term is given by f(1) = 8
Since here the  given series is arithmetic series and here common difference is given by 5-8 = -3
Recurrence relation is given by f(n+1) - f(n) = Â d
                    where d is common difference which is given  to be  -3 .
therefore  it is given as
  f(n+1) -f(n) = -3
     f(n+1) = f(n) -3    [ adding f(n) both sides]
Since n is starting from 1 there for  its fourth option is correct
f(1) =8 and , f(n+1) = f(n) -3 ) , for n ≥1
Answer:
Choice D is the correct answer.
Step-by-step explanation:
We have given a arithematic sequence.
8,5,2,-1
We have to find a recurrence relation for given sequence.
The formula for common difference of arithematic sequence is:
f(n+1)-f(n) = d where f(n) and f(n+1) are consecutive terms and d is common difference between consecutive terms.
In given sequence,
f(1) = 8 and f(2) = 5
d = -3
putting the value of d in above formula , we have
f(n+1)-f(n) = -3
Adding f(n) to both sides of above equation, we have
f(n+1)-f(n)+f(n) = f(n)-3
f(n+1) = f(n)-3
since given that n = 1
f(n+1) = f(n)-3  ; for n ≥ 1  which is the answer.
