What is the general term of the sequence (12, 15, 18, 21, …)?
Answer and explanation
Correct answer: a_n = 3n + 9
The relevant concept is the nth-term rule for an arithmetic sequence. The common difference is d = 15 − 12 = 3. Using a_n = a_1 + (n − 1)d with a_1 = 12 gives a_n = 12 + 3(n − 1) = 12 + 3n − 3 = 3n + 9. Hence option C is correct. A direct check gives a_1 = 3(1) + 9 = 12, a_2 = 15, a_3 = 18, and a_4 = 21. Option A gives 15 when n = 1, so it starts incorrectly; option B gives 12, 24, 36, …, and option D gives 12, 16, 20, …, which has a different common difference. Therefore only option C fits the entire pattern.
Frequently asked questions
What is the correct answer to this question?
a_n = 3n + 9
Why is this the correct answer?
The relevant concept is the nth-term rule for an arithmetic sequence. The common difference is d = 15 − 12 = 3. Using a_n = a_1 + (n − 1)d with a_1 = 12 gives a_n = 12 + 3(n − 1) = 12 + 3n − 3 = 3n + 9. Hence option C is correct. A direct check gives a_1 = 3(1) + 9 = 12, a_2 = 15, a_3 = 18, and a_4 = 21. Option A gives 15 when n = 1, so it starts incorrectly; option B gives 12, 24, 36, …, and option D gives 12, 16, 20, …, which has a different common difference. Therefore only option C fits the entire pattern.
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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