find the average of odd number less than 100
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Answered by
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
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
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.
Please mark brainliest............
(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.
Please mark brainliest............
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