## 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).

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).

in progress 0
7 months 2021-10-04T04:43:48+00:00 2 Answers 0 views 0

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.