Question

Determine the recursive function that defines the sequence.

Answer 1

for plato family

f(1)=4

f(n)=5. f(n-1) ,for n
`\geq` 2

Explanation:

Answer 2

Option: C is the correct answer.

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

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`