Find the average of first 97 natural numbers

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Find the average of first 97 natural numbers.

  1. A. 47
  2. B. 37
  3. C. 48
  4. D. 49

E. 49.5

Here is complete explanation of Find the average of first 97 natural numbers .

Solution(By ExamCraze Team)

1st Method:
Average of 1st n natural number is given by
$$ = frac{{ {frac{{ {{text{n}} times left( {{text{n}} + 1} right)} }}{2}} }}{{text{n}}}$$
Average of 1st 97 natural number is given by
$$eqalign{ & {frac{{ {frac{{ {97 times left( {97 + 1} right)} }}{2}} }}{{97}}} cr & = 49 cr} $$

2st 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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