Find the average of first 97 natural numbers.  Select
A) 47  B) 37  C) 48  D) 49  E) 49.5
Solution: 1st Method:   Average of 1st n natural number is given by = ([n*(n+1)]/2)/n   Average of 1st 97 natural number is given by = {([97*(97+1)]/2)/97} = 49   2nd Method:   These numbers are in AP series, so average,   ( 97*(97+1) /2)/97= 
<gadget id="calculator">( 97*(97+1) /2)/97</gadget>
<output>49</output>
49   2nd Method:   These numbers are in AP series, so average,= (sum of corresponding term)/2   = (1+97)/2= 
<gadget id="calculator">(1+97)/2</gadget>
<output>49</output>
49   Or, (2+96)/2= 49   Or, (3+95)/2 = 49 And so on.   Answer: Option 49
<result>D</result>
Find the average of first 97 natural numbers.