Question

f(n) = 2• (-3)^n

complete the recursive formula of f(n).

f(1) = ____
f(n) = f(n - 1) • ____

Answer 1

Answer:

$f(1)=-6$

$f(n)=f(n-1)(-3)$

Step-by-step explanation:

We are given that

$f(n)=2\cdot (-3)^n$

We have to complete  the recursive formula of f(n).

Substitute n=1

$f(1)=2\cdot (-3)$

$f(1)=-6$

$f(2)=2\cdot (-3)^2=18$

$f(3)=2\cdot (-3)^3=-54$

$\frac{f(2)}{f(1)}=\frac{18}{-6}=-3$

$\frac{f(3)}{f(2)}=\frac{-54}{18}=-3$

It forms geometric sequence because the ratio of two consecutive terms are equal.

Therefore, the recursive formula

$f(n)=f(n-1)r$

$f(n)=f(n-1)(-3)$

Answer 2

Answer:

f(1) = -6

f(n)= f(n−1)⋅ -3

Step-by-step explanation: