Question

-Brainliset pls help :)

Answer 1

D

Explanation:

A recursive formula lets us calculate a term in the sequence by multiplying the previous term by the common ratio r

for the sequence

- 3, 9 , - 27 , 81....

the common ratio r is

r = 9 ÷ - 3 = - 27 ÷ 9 = 81 ÷ - 27 = - 3

Then the recursive formula is

f(n) = - 3 f(n - 1) if n > 1

f(1) = - 3

option D

Answer 2

D)

Explanation:

A recursive formula always has two parts: the value of an initial term (or terms), and an equation defining
`a_n`​​ in terms of preceding terms.

From inspection, the initial term is -3

`\implies a_1=-3`

`\implies f(1)=-3`

From inspection, we can see that each term is the preceding term multiplied by -3. Therefore, the sequence can be defined as:

`a_n=-3(n-1)`

`\implies f(n)=-3f(n-1)`

So the recursive formula for the sequence is D)

`f(n)=\left \{ {{f(1)=-3} \atop {f(n)=-3f(n-1)}} \right.`