What is the sum of the first five multiples of 12?

Appeared in: AIIMS CRE, SNO-2024

Explanation

The first five multiples of 12 are 12, 24, 36, 48, and 60.
The sum of these five numbers is calculated as: 12 + 24 + 36 + 48 + 60 = 180.
Alternatively, using the formula for the sum of the first 'n' multiples of a number 'x', which is Sum = x * [n * (n + 1) / 2].
Here, x = 12 and n = 5.
Sum = 12 * [5 * (5 + 1) / 2] = 12 * [5 * 6 / 2] = 12 * 15 = 180.

Option A: This value represents only the fifth multiple of 12 (12 x 5 = 60), not the sum of the first five multiples.
Option B: This is the sum of only the first four multiples of 12 (12 + 24 + 36 + 48 = 120). The question asks for the sum of the first five.
Option D: This value is an incorrect calculation. It might result from a multiplication error or summing the wrong set of numbers.

Visual 1: Infographic - A chart showing the first five multiples of 12 on a number line and how they are added together to reach the sum of 180.
Visual 2: Formula Card - A visual card displaying the formula for the sum of an arithmetic progression: Sₙ = n/2 * (a₁ + aₙ), with each variable clearly defined.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain This question tests the ability to calculate the sum of an arithmetic series, specifically the sum of the first 'n' multiples of a given number as background academic context rather than a clinical decision trigger.
While not a clinical question, strong numeracy skills are fundamental for nurses.
Nurses use arithmetic daily for tasks like calculating medication dosages, titrating IV drips, and interpreting lab results.
Accurate calculations are critical for patient safety to prevent medication errors and ensure proper treatment delivery.

How to Approach the Question

First, carefully read the question to identify the key components: the number (12), the quantity of multiples (first five), and the required operation (sum).
List the multiples required. In this case, multiply 12 by 1, 2, 3, 4, and 5.
Add the numbers you listed: 12 + 24 + 36 + 48 + 60.
Alternatively, use a shortcut. Factor out 12: 12 * (1 + 2 + 3 + 4 + 5). Sum the numbers in the parenthesis (15) and multiply by 12.
For a faster method, apply the formula for the sum of the first 'n' multiples of 'x': Sum = x * [n * (n + 1) / 2].
Compare your final calculated sum with the given options to select the correct answer.

Concept Tested & Keywords

Concept Tested: This question tests the ability to calculate the sum of an arithmetic series, specifically the sum of the first 'n' multiples of a given number.
Stem keywords: sum, first five, multiples, 12
Lead-in keywords: What is

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