What is the nth term of the sequence (6, 9, 12, 15, ...)?
Answer and explanation
Correct answer: aₙ = 3n + 3
The terms form an arithmetic progression because the common difference is constant: 9 − 6 = 3, 12 − 9 = 3, and 15 − 12 = 3. Use the arithmetic-progression formula aₙ = a₁ + (n − 1)d. With first term a₁ = 6 and common difference d = 3, we obtain aₙ = 6 + (n − 1)3 = 6 + 3n − 3 = 3n + 3. Therefore, option A is correct. Checking n = 1 gives a₁ = 3 + 3 = 6; n = 2 gives 9; n = 3 gives 12; and n = 4 gives 15. Option B gives 3 as the first term, option C gives 0, and option D gives 7, so those alternatives fail the first-term test.
Frequently asked questions
What is the correct answer to this question?
aₙ = 3n + 3
Why is this the correct answer?
The terms form an arithmetic progression because the common difference is constant: 9 − 6 = 3, 12 − 9 = 3, and 15 − 12 = 3. Use the arithmetic-progression formula aₙ = a₁ + (n − 1)d. With first term a₁ = 6 and common difference d = 3, we obtain aₙ = 6 + (n − 1)3 = 6 + 3n − 3 = 3n + 3. Therefore, option A is correct. Checking n = 1 gives a₁ = 3 + 3 = 6; n = 2 gives 9; n = 3 gives 12; and n = 4 gives 15. Option B gives 3 as the first term, option C gives 0, and option D gives 7, so those alternatives fail the first-term 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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