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📐 Mathematics  ·  Sequences and Series  ·  JEE

The value of 1² − 2² + 3² − 4² + ... + (2n−1)² − (2n)² is:

Answer: −n(2n + 1).

  • A n(2n + 1)
  • B −n(2n + 1)
  • C −n(n + 1)
  • D n(n + 1)

Correct answer: B. −n(2n + 1)

Explanation: Grouping in pairs: (2k−1)² − (2k)² = −(4k − 1). Summing k = 1 to n gives −(2n² + n) = −n(2n + 1).

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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