Let be the arithmetic mean of the squares of the first natural numbers. If is a natural number such that" "then, the value of is

3 Explanation: 1. Define : The arithmetic mean of the squares of the first natural numbers is given by: Using the formula for the sum of the first squares, , we get: 2. Simplify the term : Substitute the expression for : 3. Evaluate the summation: We are given . Substituting our simplified expression: 4. Solve for : Testing integer values for : If : Since the equation holds true for , the value is . Correct Option: 3.

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NIMCET 2026 — Mathematics PYQ

NIMCET | Mathematics | 2026

Let $A_{k}$ be the arithmetic mean of the squares of the first $k$ natural numbers. If $n$ is a natural number such that"

$k = 1 \sum n (6 A_{k} - 3 k) = 31$

"then, the value of $n$ is

Choose the correct answer: