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If f(1) = 1 and f(n) = 3n - f(n - 1) for all integers n > 1 , then the value of f(2023) is _________
Correct Answer: 3034
Let's understand the pattern here.
F(1) = 1
F(2) = 3*2 - 1
F(3) = 3*3 - 3*2 + 1 = 3*(3-2)+1
F(4) = 3*4 - 3*3 + 3*2 - 1 = 3*(4-3)+3*2+1
F(5) = 3*5 - 3*4 + 3*3 - 3*2 + 1 = 3(5-4)+3(3-2)+1 = $$3\cdot\frac{\left(5-1\right)}{2}+1$$
For odd numbers, this can be interpreted as F(n) = $$3\cdot\frac{\left(n-1\right)}{2}+1$$
For F(2023) = $$3\cdot\frac{\left(2023-1\right)}{2}+1$$ = $$3\cdot\frac{2022}{2}+1=3\cdot1011+1\ =3034$$
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