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

Explanation:

Answer 2

`f(1)=-6`

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

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`

`(f(2))/(f(1))=(18)/(-6)=-3`

`(f(3))/(f(2))=(-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)`