Q182 / 270 · NDA 2022 (Phase 2) · Mathematics

Paragraph: Let $f(x)$ be a function satisfying $f(x+y)=f(x) f(y)$ for all $x, y$ $\in N$ such that $f(1)=2$ :Question: What is $\sum_{x=1}^5 f(2 x-1)$ equal to ?

  • A
    $341$
  • Correct answer
    B
    $682$
  • C
    $1023$
  • D
    $1364$

Solution

$\begin{aligned} & \sum_{x=1}^5 f(2 x-1)=f(1)+f(3)+f(5)+f(7)+f(9) \\ & =2+8+32+\ldots 5 \text { terms } \\ & =\frac{2\left(4^5-1\right)}{4-1}=\frac{2 \times 1023}{3}=682\end{aligned}$

Hence, the correct answer is option: 'B'.

Relevant Questions