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What is the average (arithmetic mean) of all themultiples of ten from 10 to 190 inclusive?

What is the average (arithmetic mean) of all the multiples of ten f rom 10 to 190 inclusive?

A. 90B. 95C. 100D. 105E. 110

Solution:

Arithmetic mean of all the multiples of ten f rom 10 to 190 inclusive is given by sum of all themultiples f rom 10 to 190 / 19 ==>

sum = 10+20 + 30 ..190==> take 10 as common ==> 10 (1+2+3+4 ...19)

Arithmetic mean = 10 (1+2+3+4 ...19) /19

Sum of n consecutive number is given by n(n+1)/2 ==> 19(20)/2

A.M = 19(20)/2 *10/19 ==> 100