If a_n = n(n + 3), which term is 130?
Answer and explanation
Correct answer: 10th
The governing concept is locating a term using an explicit product-form rule. We need n(n + 3) = 130. Testing the listed positions is efficient: for n = 10, a_10 = 10(10 + 3) = 10 × 13 = 130. Thus 130 is the 10th term, making option C correct. Algebraically, n² + 3n − 130 = 0, which factors as (n + 13)(n − 10) = 0. The possible roots are n = 10 and n = −13, but a sequence position must be positive, so only n = 10 is valid. The other options yield 88, 108, and 154 respectively, so they are not equal to 130.
Frequently asked questions
What is the correct answer to this question?
10th
Why is this the correct answer?
The governing concept is locating a term using an explicit product-form rule. We need n(n + 3) = 130. Testing the listed positions is efficient: for n = 10, a_10 = 10(10 + 3) = 10 × 13 = 130. Thus 130 is the 10th term, making option C correct. Algebraically, n² + 3n − 130 = 0, which factors as (n + 13)(n − 10) = 0. The possible roots are n = 10 and n = −13, but a sequence position must be positive, so only n = 10 is valid. The other options yield 88, 108, and 154 respectively, so they are not equal to 130.
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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