# Find the average of first 97 natural numbers.

A. 47

B. 37

C. 48

D. 49

E. 49.5

**Answer: Option D **

__Solution(By Examveda Team)__

1^{st}Method:

Average of 1

^{st}n natural number is given by

$$ = \frac{{ {\frac{{ {{\text{n}} \times \left( {{\text{n}} + 1} \right)} }}{2}} }}{{\text{n}}}$$

Average of 1

^{st}97 natural number is given by

$$\eqalign{ & {\frac{{ {\frac{{ {97 \times \left( {97 + 1} \right)} }}{2}} }}{{97}}} \cr & = 49 \cr} $$

2

^{st}Method:

These numbers are in AP series so average.

$$\eqalign{ & = \frac{{ {{\text{sum of corresponding term}}} }}{2} \cr & = \frac{{ {1 + 97} }}{2} = 49 \cr & {\text{or, }}\frac{{ {2 + 96} }}{2} = 49 \cr & {\text{or, }}\frac{{ {3 + 95} }}{2} = 49 \cr & {\text{And so on}}{\text{.}} \cr} $$

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A. 125 km/hr

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(n+1)/2

97+1/2=49