What is the nth term of the sequence (15, 18, 21, 24, ...)?
Answer and explanation
Correct answer: aₙ = 3n + 12
The sequence increases by a fixed amount: 18 − 15 = 3, 21 − 18 = 3, and 24 − 21 = 3. Thus it is an arithmetic sequence with first term a₁ = 15 and common difference d = 3. Applying aₙ = a₁ + (n − 1)d gives aₙ = 15 + (n − 1)3 = 15 + 3n − 3 = 3n + 12. Hence option A is correct. A reliable check is to substitute n = 1, which gives 15, and n = 4, which gives 24. Option B gives 15 at n = 1 but then jumps by 15; option C gives 18 as its first term; option D gives the correct second term by coincidence but not the correct constant difference.
Frequently asked questions
What is the correct answer to this question?
aₙ = 3n + 12
Why is this the correct answer?
The sequence increases by a fixed amount: 18 − 15 = 3, 21 − 18 = 3, and 24 − 21 = 3. Thus it is an arithmetic sequence with first term a₁ = 15 and common difference d = 3. Applying aₙ = a₁ + (n − 1)d gives aₙ = 15 + (n − 1)3 = 15 + 3n − 3 = 3n + 12. Hence option A is correct. A reliable check is to substitute n = 1, which gives 15, and n = 4, which gives 24. Option B gives 15 at n = 1 but then jumps by 15; option C gives 18 as its first term; option D gives the correct second term by coincidence but not the correct constant difference.
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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