If a_n=n^2+3n+2, what are the first four terms?
Answer and explanation
Correct answer: 6, 12, 20, 30
The governing concept is evaluating an explicit sequence rule at n=1, 2, 3 and 4. Substitute each position into a_n=n^2+3n+2: a_1=1^2+3(1)+2=6, a_2=2^2+3(2)+2=12, a_3=3^2+3(3)+2=20, and a_4=4^2+3(4)+2=30. Therefore the first four terms are 6, 12, 20 and 30, so option D is correct. Option A appears to omit part of the expression, option B does not result from the stated quadratic rule, and option C gives incorrect substitutions. The indexing starts at 1, not 0, because the first term is conventionally a_1.
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What is the correct answer to this question?
6, 12, 20, 30
Why is this the correct answer?
The governing concept is evaluating an explicit sequence rule at n=1, 2, 3 and 4. Substitute each position into a_n=n^2+3n+2: a_1=1^2+3(1)+2=6, a_2=2^2+3(2)+2=12, a_3=3^2+3(3)+2=20, and a_4=4^2+3(4)+2=30. Therefore the first four terms are 6, 12, 20 and 30, so option D is correct. Option A appears to omit part of the expression, option B does not result from the stated quadratic rule, and option C gives incorrect substitutions. The indexing starts at 1, not 0, because the first term is conventionally a_1.
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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