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NDA 2022
Exam
NDA
Year
2022
Subject
Mathematics
Chapter
Functions

NDA 2022 · Mathematics · Functions

Paragraph: Let f(x) be a function satisfying f(x+y)=f(x) f(y) for...

Paragraph: Let f(x)f(x) be a function satisfying f(x+y)=f(x)f(y)f(x+y)=f(x) f(y) for all x,y∈Nx, y\in \mathbb{N} such that f(1)=2f(1)=2 :Question: What is ∑x=15f(2x−1)\sum_{x=1}^5 f(2 x-1) equal to ?

Options

  1. A341341
  2. B682682
  3. C10231023
  4. D13641364

Correct answer

B. 682682

Step-by-step solution

∑x=15f(2x−1)=f(1)+f(3)+f(5)+f(7)+f(9)=2+8+32+…5 terms =2(45−1)4−1=2×10233=682\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}
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