The average of the first twelve multiples of 11 is:

Question

Examoogle · Accepted Answer

The correct answer is Option D: 71.5. The average of the first $n$ multiples of any number $x$ is given by $x 	imes \frac{n+1}{2}$. For $x = 11$ and $n = 12$, average = $11 	imes \frac{13}{2} = \frac{143}{2} = 70.5$.

Step-by-Step Solution & Concepts:
Shortcut Trick: The average of the first $n$ multiples of any number $x$ is given by $x 	imes \frac{n+1}{2}$. For $x = 11$ and $n = 12$, average = $11 	imes \frac{13}{2} = \frac{143}{2} = 70.5$.

Formula Used: $$	ext{Average} = 11 	imes \frac{n + 1}{2}$$

Given: First twelve multiples of 11

Steps: Understand the Series: The first twelve multiples of 11 form an arithmetic progression: $11, 22, 33, \dots, 132$, where the first term $a = 11$ and the last term $l = 12 	imes 11 = 132$.. Apply the Average Formula for AP: For any arithmetic progression, the average is the average of the first and last terms: $	ext{Average} = \frac{	ext{First term} + 	ext{Last term}}{2}$.. Calculate Final Value: Dividing $143$ by $2$ gives $70.5$.

Answer: D is correct because the average of the first twelve multiples of 11 is calculated as $\frac{11 + 132}{2} = \frac{143}{2} = 70.5$.

Exam Tip: The average of the first $n$ multiples of any number $x$ can always be quickly found using the formula $x 	imes \frac{n+1}{2}$, which applies to any arithmetic sequence.

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