Question

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?

Answer 1

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

Explanation:

Given that a=-9 and
`a_(n)=a_(n-1)-4`

The recursive formula is
`a_(n)=a_(n-1)+d`

Therefore d=-4

Let
`a_(1)=-9` and d=-4

We can find
`a_(2),a_(3),...`

`a_(2)=a_(1)+d`

`=-9-4=-13`

Therefore
`a_(2)=-13`

`a_(3)=a_(2)+d`

`=-13-4=-17`

Therefore
`a_(3)=-17` and so on.

Therefore the arithmetic sequence is
`{\{-9,-13,-17,...}\}`

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
`{\{-9,-13,-17,...}\}`

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