Question

Find the average of all even numbers from 200 to 500?

Answer 1

it's too hard to find the average.
take even number of 200 to 300 , 301 to 400 , and 401 to 500.
write even number and find average.

Answer 2

The even numbers from 200 to 500 also include 200. Therefore, the total number of even numbers in this case is (500-200)/2 +1 = 151
[+1 because we have subtracted 200 but it is also present in the series].
Now, this series of even numbers i.e., 200, 202,..., 500 is in arithmatic progression or in other words, the difference of two consecutive numbers is always 2. Hence, the middle term or this series is the average. Middle term is 76th even number starting from 200.
Thus, average =200 + 2×(76-1) =200+150 =350. [Answer]

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