Which is the nth term of the sequence −1, 4, −9, 16, −25, …?
Answer and explanation
Correct answer: (−1)ⁿ n²
The governing concept is an explicit rule for the nth term. The absolute values of the terms are 1, 4, 9, 16, and 25, which are 1², 2², 3², 4², and 5². The signs begin negative and then alternate: negative for odd n and positive for even n. Since (−1)ⁿ is negative when n is odd and positive when n is even, the required rule is aₙ = (−1)ⁿn². Checking gives a₁ = −1, a₂ = 4, a₃ = −9, and a₄ = 16. Option A gives the opposite sign, option B misses all signs, and option D does not reproduce the listed terms.
Frequently asked questions
What is the correct answer to this question?
(−1)ⁿ n²
Why is this the correct answer?
The governing concept is an explicit rule for the nth term. The absolute values of the terms are 1, 4, 9, 16, and 25, which are 1², 2², 3², 4², and 5². The signs begin negative and then alternate: negative for odd n and positive for even n. Since (−1)ⁿ is negative when n is odd and positive when n is even, the required rule is aₙ = (−1)ⁿn². Checking gives a₁ = −1, a₂ = 4, a₃ = −9, and a₄ = 16. Option A gives the opposite sign, option B misses all signs, and option D does not reproduce the listed terms.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Sequences and Progressions. Topic: nth term.
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