If aₙ = n(n − 2), which term is 48?
Answer and explanation
Correct answer: 8th
The governing concept is finding the index of a specified sequence value by solving aₙ = 48. Set n(n − 2) = 48 and expand: n² − 2n − 48 = 0. Factoring gives (n − 8)(n + 6) = 0, so n = 8 or n = −6. A term number must be a positive integer, so n = 8 is the valid solution. Therefore 48 is the eighth term and option C is correct. A quick check confirms a₈ = 8(8 − 2) = 8 × 6 = 48. The other choices give a₆ = 24, a₇ = 35, and a₉ = 63, so none of them equals 48.
Frequently asked questions
What is the correct answer to this question?
8th
Why is this the correct answer?
The governing concept is finding the index of a specified sequence value by solving aₙ = 48. Set n(n − 2) = 48 and expand: n² − 2n − 48 = 0. Factoring gives (n − 8)(n + 6) = 0, so n = 8 or n = −6. A term number must be a positive integer, so n = 8 is the valid solution. Therefore 48 is the eighth term and option C is correct. A quick check confirms a₈ = 8(8 − 2) = 8 × 6 = 48. The other choices give a₆ = 24, a₇ = 35, and a₉ = 63, so none of them equals 48.
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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