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Find the average of first 97 natural numbers.
- A. 47
- B. 37
- C. 48
- 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.
$$eqalign{
& = frac{{ {{text{sum of corresponding term}}} }}{2} cr
& = frac{{ {1 + 97} }}{2} = 49 cr
& {text{or, }}frac{{ {2 + 96} }}{2} = 49 cr
& {text{or, }}frac{{ {3 + 95} }}{2} = 49 cr
& {text{And so on}}{text{.}} cr} $$