The average of the first 21 multiples of 3 will be:

Appeared in: NHM UP Staff Nurse-2023 Shift-2nd

Explanation

The first 21 multiples of 3 form an arithmetic progression: 3, 6, 9, ..., 63.
The average of an arithmetic progression can be found by averaging the first and last terms.
Calculation: (First Term + Last Term) / 2 = (3 + 63) / 2 = 66 / 2 = 33.
Alternatively, the average of the first 'n' multiples of a number 'k' is given by the formula: k * (n + 1) / 2. Here, 3 * (21 + 1) / 2 = 33.

Option B: 29 is a miscalculation and does not represent the average of the specified sequence.
Option C: 31 is a miscalculation. It might result from an error in adding the first and last terms or in division.
Option D: 27 is the average of the first 17 multiples of 3, not the first 21.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Calculating the average of an arithmetic progression as background academic context rather than a clinical decision trigger.
While this is a mathematics question, strong numeracy skills are essential for nurses.
Nurses perform calculations daily for drug dosages, IV drip rates, and fluid balance monitoring, where accuracy is critical for patient safety.
What if? If a nurse needed to administer a total of 693 mg of a drug in 21 equal doses over a period, they would need to calculate the amount per dose (693 / 21 = 33 mg), a calculation similar to finding an average.

How to Approach the Question

First, identify what the question is asking for: the average of a set of numbers.
Recognize that 'the first 21 multiples of 3' describes an arithmetic progression (a sequence with a constant difference).
Determine the first term (3 × 1 = 3) and the last term (3 × 21 = 63) of the sequence.
Apply the formula for the average of an arithmetic progression: Average = (First Term + Last Term) / 2.
Calculate the result: (3 + 63) / 2 = 33.
Alternatively, use the shortcut formula for the average of the first 'n' multiples of 'k': k * (n + 1) / 2.

Concept Tested & Keywords

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Attempt every question from this paper in a timed mock, then review the full solution for each one.