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Question 22

If $$f(n + 1) = \frac{3 \times f(n) + 2}{3}$$ for all natural numbers $$n \ge 1$$ and $$f(1) = 2$$, then $$f(2026) = $$ ______.


Correct Answer: 1352

Solution

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The rule simplifies to $$f(n + 1) = f(n) + \frac{2}{3}$$, so the values form an arithmetic progression with common difference $$\frac{2}{3}$$. Therefore $$f(2026) = f(1) + 2025 \times \frac{2}{3} = 2 + 1350 = 1352$$.

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