If a_n = n² + 2n, which is the first term greater than 100?
Answer and explanation
Correct answer: 10th
The governing concept is finding the first sequence term that crosses a specified boundary. Because the rule a_n = n² + 2n increases for positive n, it is sufficient to check consecutive positions near 100. For n = 9, a_9 = 9² + 2(9) = 81 + 18 = 99, which is not greater than 100. For n = 10, a_10 = 10² + 2(10) = 100 + 20 = 120, which is greater than 100. Therefore the first qualifying term is the 10th term, so option B is correct. The 9th term fails the strict inequality, while later options are not the first because n = 10 already satisfies it.
Frequently asked questions
What is the correct answer to this question?
10th
Why is this the correct answer?
The governing concept is finding the first sequence term that crosses a specified boundary. Because the rule a_n = n² + 2n increases for positive n, it is sufficient to check consecutive positions near 100. For n = 9, a_9 = 9² + 2(9) = 81 + 18 = 99, which is not greater than 100. For n = 10, a_10 = 10² + 2(10) = 100 + 20 = 120, which is greater than 100. Therefore the first qualifying term is the 10th term, so option B is correct. The 9th term fails the strict inequality, while later options are not the first because n = 10 already satisfies it.
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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