If aₙ = n² + (−1)ⁿ, what is the value of a₆ − a₅?
Answer and explanation
Correct answer: 13
The governing concept is evaluating an indexed formula while handling the parity of the exponent. For n = 6, which is even, (−1)⁶ = 1, so a₆ = 6² + 1 = 36 + 1 = 37. For n = 5, which is odd, (−1)⁵ = −1, so a₅ = 5² − 1 = 25 − 1 = 24. Therefore a₆ − a₅ = 37 − 24 = 13. Option A would ignore the sign contribution in one part, option B comes from an arithmetic error, and option D does not result from the stated rule. Separating the even and odd cases prevents the common sign mistake.
Frequently asked questions
What is the correct answer to this question?
13
Why is this the correct answer?
The governing concept is evaluating an indexed formula while handling the parity of the exponent. For n = 6, which is even, (−1)⁶ = 1, so a₆ = 6² + 1 = 36 + 1 = 37. For n = 5, which is odd, (−1)⁵ = −1, so a₅ = 5² − 1 = 25 − 1 = 24. Therefore a₆ − a₅ = 37 − 24 = 13. Option A would ignore the sign contribution in one part, option B comes from an arithmetic error, and option D does not result from the stated rule. Separating the even and odd cases prevents the common sign mistake.
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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