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If f(1)=12 and f(n)=f(n-1)-4 then determine the value of f(40) ?

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Final answer:

The value of f(40), given the recursive definition f(n) = f(n-1) - 4 with a starting value of f(1)=12, is -144.

Step-by-step explanation:

Given that f(1)=12 and the function follows a recursive pattern such that f(n) = f(n-1) - 4, we can determine the value of f(40) by recognizing this as an arithmetic sequence where the common difference is -4 and the first term is 12.

To find the value of f(40), we use the formula for an arithmetic sequence:
f(n) = f(1) + (n - 1) * d, where d is the common difference and n is the term number. Plugging in the values we get: f(40) = 12 + (40 - 1) * (-4), which simplifies to: f(40) = 12 - 39 * 4.

Calculating the expression we get f(40) = 12 - 156, leading to a final result of f(40) = -144.

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