If (a_n=(-1)^n(2n+3)), what is (a_6)?
Answer and explanation
Correct answer: (15)
The governing concept is direct evaluation of an explicit sequence rule, with special attention to the parity of n. Substitute n = 6 into aₙ = (−1)ⁿ(2n + 3): a₆ = (−1)⁶(2·6 + 3). Since 6 is even, (−1)⁶ = 1, and 2·6 + 3 = 15. Hence a₆ = 1 × 15 = 15, so option A is correct. If the index had been odd, the factor (−1)ⁿ would be −1 and the result would be negative; this explains the plausible distractor −15. The values ±12 do not result from correctly evaluating 2n + 3 at n = 6.
Frequently asked questions
What is the correct answer to this question?
(15)
Why is this the correct answer?
The governing concept is direct evaluation of an explicit sequence rule, with special attention to the parity of n. Substitute n = 6 into aₙ = (−1)ⁿ(2n + 3): a₆ = (−1)⁶(2·6 + 3). Since 6 is even, (−1)⁶ = 1, and 2·6 + 3 = 15. Hence a₆ = 1 × 15 = 15, so option A is correct. If the index had been odd, the factor (−1)ⁿ would be −1 and the result would be negative; this explains the plausible distractor −15. The values ±12 do not result from correctly evaluating 2n + 3 at n = 6.
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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