Question

Find the arthmatic mean of all even no between 89 and101

Answer 1

first number is : 90
Therefore, a = 90

Last number is : 100
Therefore, an = 100

Common difference (d) = 2

Number of even numbers between them =
an = a + (n - 1) d
100 = 90 + (n - 1)2
100 - 90 = 2(n - 1)
10 = 2(n - 1)
10/2 = n - 1
5 = n - 1
5 + 1 = n
6 = n

Sum of even number between them is
Sm = n/2(a + an)
Sm = 6/2 (90 + 100)
= 3 (190)
= 570

Arthematic mean = sum / number
= 570 / 6
= 95