The average of square of natural numbers from 1 to 35 is?
Question
The average of square of natural numbers from 1 to 35 is?
Solution 1
Sure, here is the step by step solution:
The formula for the sum of squares of first n natural numbers is n*(n+1)*(2n+1)/6.
So, the sum of squares of first 35 natural numbers is 35*(35+1)(235+1)/6 = 13685.
The average of squares of these numbers is the sum divided by the count of numbers. So, the average is 13685/35 = 391.
So, the average of square of natural numbers from 1 to 35 is 391.
Solution 2
Sure, to find the average of the squares of natural numbers from 1 to 35, we need to use the formula for the sum of squares of natural numbers, which is n*(n+1)*(2n+1)/6.
Step 1: Calculate the sum of squares of natural numbers from 1 to 35. Using the formula, we get 35*(35+1)(235+1)/6 = 353671/6 = 158410.
Step 2: Calculate the average. The average is the sum divided by the number of terms. So, the average is 158410/35 = 4526.
So, the average of the squares of natural numbers from 1 to 35 is 4526.
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