What is the nth term of the sequence 4, 7, 10, 13, …?
Answer and explanation
Correct answer: aₙ = 3n + 1
Direct answer: aₙ = 3n + 1, so B is correct. Compare consecutive terms: 7 − 4 = 3, 10 − 7 = 3, and 13 − 10 = 3. The difference is constant, so this is an arithmetic sequence. For an arithmetic sequence, aₙ = a₁ + (n − 1)d, where a₁ is the first term and d is the common difference. Here a₁ = 4 and d = 3. Therefore aₙ = 4 + (n − 1)3 = 4 + 3n − 3 = 3n + 1. Check the rule: n = 1 gives 4, n = 2 gives 7, and n = 4 gives 13. A gives 2 when n = 1, so it fails immediately. C gives 4 at n = 1 but then increases by 4, not by 3. D begins with 4 but increases by only 1. Common warning: do not use 3n alone without adjusting for the first term; always test n = 1.
Frequently asked questions
What is the correct answer to this question?
aₙ = 3n + 1
Why is this the correct answer?
Direct answer: aₙ = 3n + 1, so B is correct. Compare consecutive terms: 7 − 4 = 3, 10 − 7 = 3, and 13 − 10 = 3. The difference is constant, so this is an arithmetic sequence. For an arithmetic sequence, aₙ = a₁ + (n − 1)d, where a₁ is the first term and d is the common difference. Here a₁ = 4 and d = 3. Therefore aₙ = 4 + (n − 1)3 = 4 + 3n − 3 = 3n + 1. Check the rule: n = 1 gives 4, n = 2 gives 7, and n = 4 gives 13. A gives 2 when n = 1, so it fails immediately. C gives 4 at n = 1 but then increases by 4, not by 3. D begins with 4 but increases by only 1. Common warning: do not use 3n alone without adjusting for the first term; always test n = 1.
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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