f(1) = 6, f(n) = f(n-1) +3for n ≥ 2
To find the value of f(2), we can use the given recursive formula:
f(n) = f(n-1) + 3 for n ≥ 2
Let’s plug in n = 2 into the formula:
f(2) = f(2-1) + 3
f(2) = f(1) + 3
Since we are given that f(1) is equal to 6:
f(2) = 6 + 3
f(2) = 9
Therefore, f(2) is equal to 9
To find the value of f(2), we can use the given recursive formula:
f(n) = f(n-1) + 3 for n ≥ 2
Let’s plug in n = 2 into the formula:
f(2) = f(2-1) + 3
f(2) = f(1) + 3
Since we are given that f(1) is equal to 6:
f(2) = 6 + 3
f(2) = 9
Therefore, f(2) is equal to 9.
Now, let’s find the value of f(3) using the same formula:
f(3) = f(3-1) + 3
f(3) = f(2) + 3
We already found in the previous step that f(2) is equal to 9:
f(3) = 9 + 3
f(3) = 12
Therefore, f(3) is equal to 12.
Using the recursive formula, we can continue finding the values of f(n) for other values of n by substituting f(n-1) into the formula until we reach the desired value.
Definition: Recursion refers to a mathematical or computational process that is defined in terms of itself. In this case, the recursive formula defines each term of the sequence (f(n)) using the previous term (f(n-1)) and a constant value.
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