Question

What is the average of all numbers between 11 and 80 which are divisible by 6?

Answer 1

Hi ,

12 , 18 ,24 , .... , 78 are numbers between 11 and

80 which are divisible by 6 and in A. P

first term = a = 12

common difference = a2 - a1

d = 18 - 12

d = 6

an = 78

a + ( n - 1 )d = 78

12 + ( n - 1 ) 6 = 78

divide each term with 6 , we get

2 + n - 1 = 13

n + 1 = 13

n = 13 - 1

n = 12

Sum of n terms in A.P = Sn

Sn = n/2 [ a + an ]

S12 = 12/2 [ 12 + 78 ]

= 6 × 90

= 540

Therefore ,

Required average of all numbers

between 11 and 80 which are divisible

by 6 = Sn/12

= 540/12

= 45

I hope this helps you.

: )