Question

2.

Answer 1

Answer:

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 $a_{n}=a_{n-1}-4$

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