2.
the recursive formula for a sequence of numbers is shown.
a = -9
an = an-1-4
which equation would produce the same sequence of numbers as the recursive formula shown?
a. f(n) = -5 -4n
b. f(n) = -5n - 4
c. f(n) = – 9n
d. f(n) = n - 4

work?

Option A) f(n)=-5-4n is correct.

The equation would produce the same sequence of numbers as the recursive formula is f(n)=-5-4n

Step-by-step explanation:

Given that a=-9 and

The recursive formula is

Therefore d=-4

Let and d=-4

We can find

Therefore

Therefore  and so on.

Therefore the arithmetic sequence is

Option A) f(n)=-5-4n is correct.

f(n)=-5-4n

put n=1 in f(n)=-5-4n

f(1)=-5-4(1)

=-9

Therefore f(1)=-9

put n=2 in f(n)=-5-4n

f(21)=-5-4(2)

=-5-8

Therefore f(2)=-13

put n=3 we get f(n)=-5-4n

f(3)=-5-4(3)

=-5-12

Therefore f(3)=-17  and so on .

Therefore the sequence is  

Therefore the equation would produce the same sequence of numbers as the recursive formula is f(n)=-5-4n