Which option gives the first four terms of a_n = n(n + 3)?
Answer and explanation
Correct answer: 4, 10, 18, 28
The governing concept is direct substitution into an explicit product-form sequence rule. Use n = 1, 2, 3, and 4. We obtain a_1 = 1(1 + 3) = 4, a_2 = 2(2 + 3) = 10, a_3 = 3(3 + 3) = 18, and a_4 = 4(4 + 3) = 28. Therefore option B gives the first four terms. Option A begins with the value for n = 0, while option C corresponds to n(n + 1), not n(n + 3). Option D does not follow the stated multiplication rule. Keeping the two factors visible reduces errors when substituting each index.
Frequently asked questions
What is the correct answer to this question?
4, 10, 18, 28
Why is this the correct answer?
The governing concept is direct substitution into an explicit product-form sequence rule. Use n = 1, 2, 3, and 4. We obtain a_1 = 1(1 + 3) = 4, a_2 = 2(2 + 3) = 10, a_3 = 3(3 + 3) = 18, and a_4 = 4(4 + 3) = 28. Therefore option B gives the first four terms. Option A begins with the value for n = 0, while option C corresponds to n(n + 1), not n(n + 3). Option D does not follow the stated multiplication rule. Keeping the two factors visible reduces errors when substituting each index.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Sequences and Progressions. Topic: Explicit or general rule.
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