Sets, Relations & Functions
General
Grade 11
Question:
<p><span class="math-inline">\(f(x+y)=f(x)f(y)\)</span>, <span class="math-inline">\(f(1)=3\)</span>. If <span class="math-inline">\(\sum_{i=1}^n f(i)=363\)</span>, find <span class="math-inline">\(n\)</span>.</p>
Step-by-Step Solution
Key Concept: General
<div class="solution"><p>f(i)=3ⁱ. Sum=(3^{n+1}-3)/2=363 → 3^{n+1}=729=3⁶ → n=5.</p><div class="key-concept"><strong>Key Concept:</strong> Geometric sum formula</div></div>
Correct Answer: 5