Question

If f(1)=8f(1)=8 and f(n)=4f(n-1)+1f(n)=4f(n−1)+1 then find the value of f(4)f(4).

Answer 1

Answer:

f(4) = 533

Step-by-step explanation:

Answer 2

Answer:

f(4) = 533

Step-by-step explanation:

The sequence in this problem is defined as:

$f(n)=4f(n-1)+1$

where

$f(n)$ is the nth-term of the sequence

$f(n-1)$ is the (n-1)th term of the sequence

Here we also know that

$f(1)=8$

Therefore, we can find the following terms of the sequence by substituting the output of the previous term in the sequence. For instance, the term f(2) is calculated by substituting 8 into f(n-1). Then we find:

$f(2)=4f(2-1)+1=4f(1)+1=4\cdot 8+1=33$

$f(3)=4f(2)+1=4\cdot 33+1=133$

$f(4)=4f(3)+1=4\cdot 133 +1=533$

So, the term f(4) is 533.