Question

-Brainliset pls help :)

Answer 1

Answer:

D

Step-by-step 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

Answer:

D)

Step-by-step 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)

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