Finding Average of First 165 Even Numbers
The question asks for the average of the first 165 even numbers.
Mathematical Approach
The sequence of the first $N$ even numbers is: 2, 4, 6, ..., $2N$.
Here, $N = 165$. The sequence starts at 2 and ends at $2 \times 165 = 330$.
A key property is that the average of the first $N$ even numbers is simply $N + 1$.
Reasoning: The sum of the first $N$ even numbers is $N(N+1)$. The average is the sum divided by the count ($N$), which gives $\frac{N(N+1)}{N} = N+1$.
Calculating the Average
Apply the formula Average $= N + 1$ where $N = 165$.
Average $= 165 + 1$
Average $= 166$
Thus, the average of the first 165 even numbers is 166.
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Important Questions from Average
The average of 28 numbers is 77. The average of first 14 numbers is 74 and the average of last 15 numbers is 84. If the 14 th number is excluded, then what is the average of remaining numbers? (correct to one decimal places)
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Out of 6 numbers, the sum of the first 5 numbers is 7 times the 6 th number. If their average is 136, then the 6 th number is:
The average of five numbers is 30. If one number is excluded, then average becomes 31. What is the excluded number?
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