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📐 Mathematics  ·  Sequences and Series  ·  JEE

Sum: 1² + 3² + 5² + ... + (2n-1)² =

Answer: n(2n-1)(2n+1)/3.

  • A n(2n-1)(2n+1)/3
  • B n(n+1)(2n+1)/6
  • C n²(n+1)
  • D 2n(n+1)(2n+1)/3

Correct answer: A. n(2n-1)(2n+1)/3

Explanation: Sum of squares of first n odd numbers = n(2n-1)(2n+1)/3. Derived by subtracting sum of even squares from total sum of squares.

Each bar grows by the common difference d=3a1=2a2=5a3=8a4=11d=3

Bar heights for AP 2, 5, 8, 11 with the common difference d=3 marked between consecutive terms.

Concept context

Arithmetic progressions, geometric progressions, and sums

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