What is the nth term of the sequence (6, 9, 12, 15, ...)?
Answer and explanation
Correct answer: aₙ = 3n + 3
The governing concept is the nth term of an arithmetic progression. Consecutive terms differ by a constant amount: 9 − 6 = 3, 12 − 9 = 3, and 15 − 12 = 3. Therefore, the first term is a₁ = 6 and the common difference is d = 3. Using aₙ = a₁ + (n − 1)d, we obtain aₙ = 6 + (n − 1)3 = 6 + 3n − 3 = 3n + 3. Hence option A is correct. Substitution confirms the rule: n = 1 gives 6, n = 2 gives 9, n = 3 gives 12, and n = 4 gives 15. Option B begins with 3, option C begins with 0, and option D begins with 7 and has difference 1, so each distractor fails either the first-term test or the common-difference test.
Frequently asked questions
What is the correct answer to this question?
aₙ = 3n + 3
Why is this the correct answer?
The governing concept is the nth term of an arithmetic progression. Consecutive terms differ by a constant amount: 9 − 6 = 3, 12 − 9 = 3, and 15 − 12 = 3. Therefore, the first term is a₁ = 6 and the common difference is d = 3. Using aₙ = a₁ + (n − 1)d, we obtain aₙ = 6 + (n − 1)3 = 6 + 3n − 3 = 3n + 3. Hence option A is correct. Substitution confirms the rule: n = 1 gives 6, n = 2 gives 9, n = 3 gives 12, and n = 4 gives 15. Option B begins with 3, option C begins with 0, and option D begins with 7 and has difference 1, so each distractor fails either the first-term test or the common-difference test.
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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