Find the sum of squares of first 8 natural numbers (i.e., 1^2 + 2^2 + \dots + 8^2).

Appeared in: RRB Staff Nurse Kolkata-2015

Explanation

The problem requires calculating the sum of the squares of the first 8 natural numbers (1² + 2² + ... + 8²).
The standard formula for the sum of the squares of the first 'n' natural numbers is Sum = n(n+1)(2n+1) / 6.
Substituting n = 8 into the formula gives: Sum = (8 * (8+1) * (2*8+1)) / 6.
This simplifies to (8 * 9 * 17) / 6.
Further calculation leads to (72 * 17) / 6 = 12 * 17 = 204.

Option A: This is an incorrect result obtained through a calculation error.
Option B: This is another incorrect result due to a miscalculation.
Option D: This value (72) is the product of the first part of the numerator (n * (n+1) = 8 * 9 = 72). The calculation is incomplete as it omits multiplying by (2n+1) and dividing by 6.

Visual 1: Formula - An infographic displaying the formula for the sum of squares of the first n natural numbers: Sum = n(n+1)(2n+1)/6.
Visual 2: Table - A step-by-step calculation table showing the square of each number from 1 to 8 and their cumulative sum.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Sum of the squares of the first n natural numbers as background academic context rather than a clinical decision trigger.
While this is a mathematics question, strong numeracy and calculation skills are fundamental for nurses.
Nurses frequently perform calculations for medication dosages, IV drip rates, and fluid balance monitoring, where accuracy is critical for patient safety.
What if? If the question asked for the sum of the first 8 natural numbers (not their squares), the formula would be n(n+1)/2, and the answer would be 8(9)/2 = 36.

How to Approach the Question

First, identify that the question asks for the 'sum of squares' of a sequence of natural numbers.
Recall the specific formula for the sum of the squares of the first 'n' natural numbers: Sum = n(n+1)(2n+1)/6.
Identify the value of 'n' from the question, which is 8.
Substitute n=8 into the formula: Sum = (8 * (8+1) * (2*8+1)) / 6.
Carefully perform the arithmetic operations: (8 * 9 * 17) / 6 = 1224 / 6 = 204.
Alternatively, for a small number like 8, you can manually square each number and add them: 1+4+9+16+25+36+49+64 = 204.

Concept Tested & Keywords

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Practise the full RRB Staff Nurse Kolkata-2015

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