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

Appeared in: RRB Staff Nurse Kolkata-2015

Explanation

The series 3, 9, 15, 21... is an Arithmetic Progression (AP) because there is a constant difference between consecutive terms.
The first term (a) is 3, and the common difference (d) is 6 (since 9 - 3 = 6).
The formula for the n-th term of an AP is Tₙ = a + (n - 1)d.
Substituting the values for the 21st term (n=21): T₂₁ = 3 + (21 - 1) × 6.
Calculation: T₂₁ = 3 + (20 × 6) = 3 + 120 = 123.

Option B: This result is obtained if the formula is incorrectly applied as a + (n × d), without subtracting 1 from n. Calculation: 3 + (21 × 6) = 129.
Option C: This result is obtained by incorrectly calculating (n-2) instead of (n-1). Calculation: 3 + (21 - 2) × 6 = 3 + 19 × 6 = 117.
Option D: This result is obtained by incorrectly calculating (n+1) instead of (n-1). Calculation: 3 + (21 + 1) × 6 = 3 + 22 × 6 = 135.

Visual 1: Infographic: A visual breakdown of the formula for the n-th term of an Arithmetic Progression (Tₙ = a + (n - 1)d), defining each component (Tₙ, a, n, d).

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 (AP) as background academic context rather than a clinical decision trigger.
This question tests basic mathematical aptitude, a skill necessary for various nursing calculations, such as drug dosage, IV drip rates, and interpreting patient data charts.
While not a direct clinical scenario, strong numeracy skills prevent medication errors and ensure patient safety.
What if the series decreased instead of increased? If the series was 21, 15, 9..., the common difference (d) would be -6, and the 21st term would be 21 + (20 × -6) = 21 - 120 = -99.

How to Approach the Question

First, analyze the given series (3, 9, 15, 21...) to identify the pattern. Notice that each term increases by a fixed number.
Recognize this pattern as an Arithmetic Progression (AP).
Identify the first term (a), which is 3.
Calculate the common difference (d) by subtracting any term from the next term (e.g., 9 - 3 = 6).
Recall the standard formula for the n-th term of an AP: Tₙ = a + (n - 1)d.
Substitute the known values (a=3, d=6, n=21) into the formula and solve for the 21st term.

Concept Tested & Keywords

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