What is the nth term of the sequence (12, 15, 18, 21, ...)?
Answer and explanation
Correct answer: aₙ = 3n + 9
This is an arithmetic sequence because the difference between consecutive terms is constant: 15 − 12 = 3, 18 − 15 = 3, and 21 − 18 = 3. For an arithmetic sequence, the nth-term rule is aₙ = a₁ + (n − 1)d. Here a₁ = 12 and d = 3, so aₙ = 12 + (n − 1)3 = 12 + 3n − 3 = 3n + 9. Therefore option A is correct. Substituting n = 1 gives 12, n = 2 gives 15, and n = 3 gives 18. Option B has the wrong growth and first term; option C gives 15 at n = 1; option D gives 12 at n = 1 but increases by 15, not 3.
Frequently asked questions
What is the correct answer to this question?
aₙ = 3n + 9
Why is this the correct answer?
This is an arithmetic sequence because the difference between consecutive terms is constant: 15 − 12 = 3, 18 − 15 = 3, and 21 − 18 = 3. For an arithmetic sequence, the nth-term rule is aₙ = a₁ + (n − 1)d. Here a₁ = 12 and d = 3, so aₙ = 12 + (n − 1)3 = 12 + 3n − 3 = 3n + 9. Therefore option A is correct. Substituting n = 1 gives 12, n = 2 gives 15, and n = 3 gives 18. Option B has the wrong growth and first term; option C gives 15 at n = 1; option D gives 12 at n = 1 but increases by 15, not 3.
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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