Question

Let $f(x)$ be a function such that $f(x+y)=f(x) \cdot f(y)$ for all $x, y \in$ N If $f(1)=3$ and $\displaystyle\sum_{k=1}^n f(k)=3279$, then the value of $n$ is

• A. 8
• B. 6
• C. 7
• D. 9

Answer 1

Answer: (C)

7

Answer 2

The correct answer is (C) : 7
f(x+y)=f(x)⋅f(y)∀x,y∈N,f(1)=3
f(2)=f2(1)=32
f(3)=f(1)f(2)=33
f(4)=34
f(k)=3k
k=1∑n​f(k)=3279
f(1)+f(2)+f(3)+………+f(k)=3279
3+32+33+………3k=3279
3−13(3k−1)​=3279
23k−1​=1093
3k−1=2186
3k=2187
k=7