what will be the average of the square of first 100 multiples of 3
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Answer:
33.333333333333333333
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This requires that you know how to calculate the sum of an arithmetic progression(an A.P.). Its easy to see that there are 33 multiples of 3 between 1 and 100 as 3*33=99 which is the nearest multiple of 3 less than 100. The A.P. will look like:
3, 6, 9, 12,…………., 96, 99
So, we have the first term as 3, common difference as 3 and number of terms as 33, just put them into the formula S= n(2a + (n-1)d)/2 where n=number of terms, a=first term and d=common difference, to get the answer as 1683.
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