If a_n = n^2 + 5n - 2, which term is equal to 148?
Answer and explanation
Correct answer: 10th
The governing concept is using an explicit nth-term rule to identify the position of a given value. We set the formula equal to 148: n^2 + 5n - 2 = 148, so n^2 + 5n - 150 = 0. Factoring gives (n + 15)(n - 10) = 0, so n = 10 or n = -15. Since a term number must be a positive integer, n = 10 is the valid solution. Direct substitution confirms it: a_10 = 10^2 + 5(10) - 2 = 100 + 50 - 2 = 148. Therefore option D is correct. The negative root is rejected because sequence positions are counted as 1, 2, 3, and so on; options A, B, and C do not produce 148.
Frequently asked questions
What is the correct answer to this question?
10th
Why is this the correct answer?
The governing concept is using an explicit nth-term rule to identify the position of a given value. We set the formula equal to 148: n^2 + 5n - 2 = 148, so n^2 + 5n - 150 = 0. Factoring gives (n + 15)(n - 10) = 0, so n = 10 or n = -15. Since a term number must be a positive integer, n = 10 is the valid solution. Direct substitution confirms it: a_10 = 10^2 + 5(10) - 2 = 100 + 50 - 2 = 148. Therefore option D is correct. The negative root is rejected because sequence positions are counted as 1, 2, 3, and so on; options A, B, and C do not produce 148.
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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