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)
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.
$$\eqalign{ & = \frac{{ {{\text{sum of corresponding term}}} }}{2} \cr & = \frac{{ {1 + 97} }}{2} = 49 \cr & {\text{or, }}\frac{{ {2 + 96} }}{2} = 49 \cr & {\text{or, }}\frac{{ {3 + 95} }}{2} = 49 \cr & {\text{And so on}}{\text{.}} \cr} $$
Join The Discussion
Comments ( 1 )
Related Questions on Average
A. 125 km/hr
B. 75 km/hr
C. 135 km/hr
D. 120 km/hr
(n+1)/2
97+1/2=49