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6 from 6 to 510 inclusive

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by sanju09 » Sat Jun 19, 2010 12:31 am
What is the average (arithmetic mean) of all multiples of 6 from 6 to 510 inclusive?
(A) 252
(B) 258
(C) 516
(D) 1510
(E) 1530
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by amising6 » Sat Jun 19, 2010 12:44 am
sanju09 wrote:What is the average (arithmetic mean) of all multiples of 6 from 6 to 510 inclusive?
(A) 252
(B) 258
(C) 516
(D) 1510
(E) 1530
so basically of the number of form 6K where k will take value of 1,2,3 integer to give the multiple of 6
so first will be 6 i.e k=1 and last willl 510/6= i.e k= 85
so total number of terms 85
sum of all the terms =(85/2) *(516)
now artihmetic mean=(85*258)/85=258

arithmetic means =258
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by sanju09 » Sat Jun 19, 2010 12:47 am
in more simple words?
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by amising6 » Sat Jun 19, 2010 12:55 am
sanju09 wrote:in more simple words?
first observation is both 6 and 510 divisible by 6
so it is a APseries with 6 as first term and common difference of 6

6,12,18,24,................510
now 510 will be 85 th term
and then formula of sum to get sum as 85*256
then arithmetic mean =sum/number of term
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by sanju09 » Sat Jun 19, 2010 1:09 am
amising6 wrote:
sanju09 wrote:in more simple words?
first observation is both 6 and 510 divisible by 6
so it is a APseries with 6 as first term and common difference of 6

6,12,18,24,................510
now 510 will be 85 th term
and then formula of sum to get sum as 85*256
then arithmetic mean =sum/number of term
Can we say that the average of terms in an AP is the average of its first and last terms?
The mind is everything. What you think you become. -Lord Buddha



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by amising6 » Sat Jun 19, 2010 1:11 am
yup bingo that is the proeprties of an ap series
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by pradeepkaushal9518 » Sat Jun 19, 2010 8:19 am
simple method i learnt

first term 6 and last 510
arithmetic mean= first+last/2 = 6+510/2=258
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