Question

If f (1) = 1 and f(n) = f(n - 1)? + 3 then find the value of f(4).

Answer 1

$f(4)=364$

Explanation

$f\mleft(n\mright)=f\mleft(n-1\mright)^2+3$

In a recursive formula, each term is defined as a function of its preceding term(s). A recursive formula designates the starting term, a1, and the nth term of the sequence, an

so, we can find the first 4 terms

Step 1

$\begin{gathered} f\mleft(n\mright)=f\mleft(n-1\mright)^2+3 \\ f(1)=1 \\ f(2)=f(2-1)^2+3 \\ f(2)=f(1)^2+3 \\ f(2)=(1)^2+3 \\ f(2)=4 \\ f(3)=f(3-1)^2+3 \\ f(3)=f(2)^2+3 \\ f(3)=(4)^2+3 \\ f(3)=19 \\ f(4)=f(4-1)^2+3 \\ f(4)=f(3)^2+3 \\ f(4)=(19)^2+3 \\ f(4)=364 \end{gathered}$

hence, the answer is

$f(4)=364$

I hope this helps you