If f(1)=4 and f(n)=f(n-1)+3 then find the value of f(5). Answer:

Base Case: We are given that f(1) = 4. This is our base case.Recursive Formula: We are also given a recursive formula: f(n) = f(n-1) + 3. This means that to find f(n), we need to know the value of f(n-1) and then add 3 to it.Finding f(2): To find f(2), we use the recursive formula with n=2: f(2) = f(2-1) + 3 = f(1) + 3. We know that f(1) = 4, so f(2) = 4 + 3 = 7.Finding f(3): To find f(3), we use the recursive formula with n=3: f(3) = f(3-1) + 3 = f(2) + 3. We found that f(2) = 7, so f(3) = 7 + 3 = 10.Finding f(4): To find f(4), we use the recursive formula with n=4: f(4) = f(4-1) + 3 = f(3) + 3. We found that f(3) = 10, so f(4) = 10 + 3 = 13.Finding f(5): To find f(5), we use the recursive formula with n=5: f(5) = f(5-1) + 3 = f(4) + 3. We found that f(4) = 13, so f(5) = 13 + 3 = 16.

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Q. If

f(1)=4

and

f(n)=f(n-1)+3

then find the value of

f(5)

\newline

Answer:

Base Case: We are given that $f(1) = 4$ . This is our base case.
Recursive Formula: We are also given a recursive formula: $f(n) = f(n-1) + 3$ . This means that to find $f(n)$ , we need to know the value of $f(n-1)$ and then add $3$ to it.
Finding $f(2)$ : To find $f(2)$ , we use the recursive formula with $n=2$ : $f(2) = f(2-1) + 3 = f(1) + 3$ . We know that $f(1) = 4$ , so $f(2) = 4 + 3 = 7$ .
Finding $f(3)$ : To find $f(3)$ , we use the recursive formula with $n=3$ : $f(3) = f(3-1) + 3 = f(2) + 3$ . We found that $f(2) = 7$ , so $f(3) = 7 + 3 = 10$ .
Finding $f(4)$ : To find $f(4)$ , we use the recursive formula with $n=4$ : $f(4) = f(4-1) + 3 = f(3) + 3$ . We found that $f(3) = 10$ , so $f(4) = 10 + 3 = 13$ .
Finding $f(5)$ : To find $f(5)$ , we use the recursive formula with $n=5$ : $f(5) = f(5-1) + 3 = f(4) + 3$ . We found that $f(4) = 13$ , so $f(5) = 13 + 3 = 16$ .