Answer:
f(4) = 533
Step-by-step explanation:
The sequence in this problem is defined as:
[tex]f(n)=4f(n-1)+1[/tex]
where
[tex]f(n)[/tex] is the nth-term of the sequence
[tex]f(n-1)[/tex] is the (n-1)th term of the sequence
Here we also know that
[tex]f(1)=8[/tex]
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:
[tex]f(2)=4f(2-1)+1=4f(1)+1=4\cdot 8+1=33[/tex]
[tex]f(3)=4f(2)+1=4\cdot 33+1=133[/tex]
[tex]f(4)=4f(3)+1=4\cdot 133 +1=533[/tex]
So, the term f(4) is 533.
