Which general term is correct for the sequence (11, 20, 29, 38, …)?
Answer and explanation
Correct answer: aₙ = 9n + 2
This is an arithmetic sequence because each term increases by the same amount: 20 − 11 = 9, 29 − 20 = 9, and 38 − 29 = 9. For an arithmetic sequence, the explicit rule is aₙ = a₁ + (n − 1)d, where a₁ is the first term and d is the common difference. Substituting a₁ = 11 and d = 9 gives aₙ = 11 + 9(n − 1) = 11 + 9n − 9 = 9n + 2. Therefore, option B is correct. Checking n = 1 gives 11, n = 2 gives 20, and n = 3 gives 29. Option A has the wrong growth, while options C and D fail even at the first term.
Frequently asked questions
What is the correct answer to this question?
aₙ = 9n + 2
Why is this the correct answer?
This is an arithmetic sequence because each term increases by the same amount: 20 − 11 = 9, 29 − 20 = 9, and 38 − 29 = 9. For an arithmetic sequence, the explicit rule is aₙ = a₁ + (n − 1)d, where a₁ is the first term and d is the common difference. Substituting a₁ = 11 and d = 9 gives aₙ = 11 + 9(n − 1) = 11 + 9n − 9 = 9n + 2. Therefore, option B is correct. Checking n = 1 gives 11, n = 2 gives 20, and n = 3 gives 29. Option A has the wrong growth, while options C and D fail even at the first term.
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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