Math, asked by ridzz2, 1 year ago

find the average of odd number less than 100

Answers

Answered by YadavShashi
1
ODD NUMBERS BETWEEN 0 TO 100 ARE

1,3,5,7……..,99

HERE THESE ARE IN AP

WHERE a = 1

d = 2

So An = a + (n-1)d

99 = 1 + (n-1) 2

98 = (n-1)2

n-1 = 49 => n = 50

Then

Sn = (n/2) * (a + An)

=( 50/2 )* (1+99)

= 25 * 100

= 2500

Average = Sn/ n

= 2500 / 50

= 50
Answered by AnnyM
1
We can add up the numbers 1, 3, ..., 99, then divide by 50:

(1 + 3 + 5.... + 99) / 50
= (1 + 99) + ( 3 + 97)..... /50
= 100 + 100 + 100.../50
= 100 * 25 / 50
= 50


(there are 25 pairs of 100, simply obtained by counting the number of elements in the set {1, 3, 5, ..., 49})

So the average of all these numbers is 50. This makes sense, because 50 is halfway between 0 and 100.



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