Find the 21st term of the following series? 3, 9, 15, 21

Appeared in: NHM UP Staff Nurse - 2019

Explanation

The given series (3, 9, 15, 21, ...) is an Arithmetic Progression (AP) because there is a constant difference of 6 between consecutive terms.
In this AP, the first term (a) is 3, and the common difference (d) is 6.
The formula to find the nth term (a_n) of an AP is a_n = a + (n - 1)d.
To find the 21st term (n=21), we substitute the values: a₂₁ = 3 + (21 - 1) × 6.
Solving the equation gives: 3 + (20 × 6) = 3 + 120 = 123.

Option B: This result is obtained by incorrectly calculating a + (n × d) instead of a + (n - 1) × d. The calculation would be 3 + (21 × 6) = 3 + 126 = 129. The formula requires subtracting 1 from the term position 'n' before multiplying by the common difference.
Option C: This would be the 20th term of the series, not the 21st. The calculation is 3 + (20 - 1) × 6 = 3 + 19 × 6 = 3 + 114 = 117.
Option D: This would be the 23rd term of the series. The calculation is 3 + (23 - 1) × 6 = 3 + 22 × 6 = 3 + 132 = 135.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Finding the nth term of an Arithmetic Progression as background academic context rather than a clinical decision trigger.
This question tests basic mathematical aptitude, a skill required for various calculations in nursing, such as drug dosage and IV drip rates.
Accuracy in sequential calculations is fundamental to preventing medication errors and ensuring patient safety.
What if the question asked for the sum of the first 21 terms? The formula would change to S_n = n/2 × [2a + (n-1)d], yielding a different result: S₂₁ = 21/2 × [2×3 + (21-1)×6] = 10.5 × [6 + 120] = 10.5 × 126 = 1323.

How to Approach the Question

Step 1: Analyze the given series (3, 9, 15, 21) to identify the pattern by calculating the difference between consecutive terms.
Step 2: Recognize that a constant difference (9-3=6, 15-9=6) indicates it is an Arithmetic Progression (AP).
Step 3: Identify the key components from the series and the question: the first term (a=3), the common difference (d=6), and the term number to find (n=21).
Step 4: Recall the standard formula for the nth term of an AP: a_n = a + (n - 1)d.
Step 5: Substitute the identified values into the formula: a₂₁ = 3 + (21 - 1) × 6.
Step 6: Perform the calculation step-by-step: 3 + (20 × 6) = 3 + 120 = 123. Finally, match this result with the given options.

Concept Tested & Keywords

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