Question

Given the recursive function f(n) = f(n - 1) - 3 ; f(1) = 9 , what would be the first three terms of the sequence ?

Answer 1

Answer:

The first three terms of the given sequence are:

$f(1)=9,f(2)=6\ and\ f(3)=3$

Step-by-step explanation:

Given:

A recursive function is given as:

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

The first term is $f(1)=9$

We need to find the remaining two terms $f(2)\ and\ f(3)$

In order to find  $f(2)\ and\ f(3)$, we put $n=2$ and $n=3$ and simplify the recursive function.

For $n=2$, the recursive function is given as:

$f(2)=f(2-1)-3\\f(2)=f(1)-3\\f(2)=9-3=6........[\because f(1)=9]$

Therefore, the second term is $f(2)=6$

For $n=3$, the recursive function is given as:

$f(3)=f(3-1)-3\\f(3)=f(2)-3\\f(2)=6-3=3........[\because f(2)=6]$

Therefore, the third term is $f(3)=3$

Hence, the first three terms of the given sequence are:

$f(1)=9,f(2)=6\ and\ f(3)=3$