Question

Determine the recursive function that defines the sequence.

Answer 1

Answer:

Option: C is the correct answer.

    C.   $f(1)=4\\\\f(n)=5\cdot f(n-1)\ ;\ n\geq 2$  

Step-by-step explanation:

Recursive Formula--

It is the formula which is used to represent the nth term of a sequence in terms of (n-1)th term of the sequence.

Here we are given a table of values by:

            n            f(n)

            1              4

            2             20

            3             100  

i.e. when n=1 we have:

$f(1)=4$

Also,

$f(2)=20\\\\i.e.\\\\f(2)=5\cdot 4\\\\i.e.\\\\f(2)=5\cdot f(1)$

Also,

$f(3)=100\\\\i.e.\\\\f(3)=5\cdot 20\\\\i.e.\\\\f(3)=5\cdot f(2)$

Hence, the recursive formula is:

$f(n)=5\cdot f(n-1)\ for\ n\geq 2$