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NDA 2021
Exam
NDA
Year
2021
Subject
Mathematics
Chapter
Sequences and Series

NDA 2021 · Mathematics · Sequences and Series

What is the mean of natural numbers contained in the interval...

What is the mean of natural numbers contained in the interval [15,64][15,64] ?

Options

  1. A36.8
  2. B38.3
  3. C39.5
  4. D40.3

Correct answer

C. 39.5

Step-by-step solution

Natural numbers contained between [15,64][15,64] numbers: 15,16,1715,16,17, 64\qquad 64 T_n=a+(n-1) d64=15(n-1) 1n−1=64−15n=50Sn=n2[a+l]=502[15+64]Sn=1975Meanof1n-1=64-15n=50\begin{gathered}S_n=\frac{n}{2}[a+l]=\frac{50}{2}[15+64] \\ S_n=1975 \end{gathered}Mean ofthe Numbers, xˉ=∑xin=Snn=197550∴xˉ=39.5\begin{aligned} & \bar{x}=\frac{\sum x_i}{n}=\frac{S_n}{n}=\frac{1975}{50} \\ & \therefore \bar{x}=39.5 \end{aligned}
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