Question : What is the average of the squares of the first five natural numbers?
Option 1: 11.5
Option 2: 10
Option 3: 12.5
Option 4: 11
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Correct Answer: 11
Solution : The sum of the square of first $n$ natural numbers = $\frac{n(n+1)(2n+1)}{6}$, where $n$ is the number of numbers. Here, $n = 5$ ⇒ Sum = $\frac{5(5+1)(10+1)}{6}=\frac{5(6)(11)}{6}=55$ $\therefore$ Average $=\frac{55}{5}=11$ Hence, the correct answer is 11.
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Question : What is the average of first 10 natural numbers?
Option 1: 5.5
Option 3: 5
Option 4: 10.5
Question : What is the average of the first 10 even numbers?
Option 1: 12
Option 3: 13
Question : The average of five consecutive odd numbers is 15. What is the smallest of these five numbers?
Option 1: 11
Option 2: 13
Option 3: 15
Option 4: 9
Question : What is the average of the first five multiples of 11?
Option 2: 55
Option 3: 33
Option 4: 22
Question : There are 32 consecutive natural numbers. The average of the first 13 numbers is $x$. What is the average of the next 19 numbers?
Option 1: $x+15$
Option 2: $x+16$
Option 3: $x+17$
Option 4: $x+18$
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