Sets, Relations & Functions
General
Grade 11
Question:
<p>\(f(x+y)=f(x)f(y)\), \(f(1)=3\). If \(\sum_{i=1}^n f(i)=363\), find \(n\).</p>
Step-by-Step Solution
<div class="solution"><p>f(i)=3ⁱ. Sum=(3^{n+1}-3)/2=363 \to 3^{n+1}=729=3^6 \to n=5.</p><div class="key-concept"><strong>Key Concept:</strong> Geometric sum formula
Correct Answer: 5