The sequence (3, 8, 15, 24, …) has general term a_n = n² + 2n. Which term is 168?
Answer and explanation
Correct answer: 12th
The governing concept is identifying a term number from an explicit, or general, rule. We need an integer n for which a_n = n² + 2n equals 168. Substitute the possible position n = 12: a_12 = 12² + 2(12) = 144 + 24 = 168. Therefore, 168 is the 12th term, so option C is correct. Checking nearby positions confirms the choice: a_11 = 121 + 22 = 143 and a_13 = 169 + 26 = 195, so neither adjacent position gives 168. The other options result from using an incorrect position or arithmetic.
Frequently asked questions
What is the correct answer to this question?
12th
Why is this the correct answer?
The governing concept is identifying a term number from an explicit, or general, rule. We need an integer n for which a_n = n² + 2n equals 168. Substitute the possible position n = 12: a_12 = 12² + 2(12) = 144 + 24 = 168. Therefore, 168 is the 12th term, so option C is correct. Checking nearby positions confirms the choice: a_11 = 121 + 22 = 143 and a_13 = 169 + 26 = 195, so neither adjacent position gives 168. The other options result from using an incorrect position or arithmetic.
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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