What is the nth term of the sequence (1, 4, 7, 10, ...)?
Answer and explanation
Correct answer: aₙ = 3n − 2
This sequence is an arithmetic progression because consecutive differences are constant: 4 − 1 = 3, 7 − 4 = 3, and 10 − 7 = 3. The nth-term rule is aₙ = a₁ + (n − 1)d. Here a₁ = 1 and d = 3, so aₙ = 1 + (n − 1)3 = 1 + 3n − 3 = 3n − 2. Therefore option B is correct. Substitution verifies the rule: n = 1 gives 1, n = 2 gives 4, n = 3 gives 7, and n = 4 gives 10. Option A begins with 4, option C has common difference 1, and option D begins with 1 but has common difference 4, so none describes the complete sequence.
Frequently asked questions
What is the correct answer to this question?
aₙ = 3n − 2
Why is this the correct answer?
This sequence is an arithmetic progression because consecutive differences are constant: 4 − 1 = 3, 7 − 4 = 3, and 10 − 7 = 3. The nth-term rule is aₙ = a₁ + (n − 1)d. Here a₁ = 1 and d = 3, so aₙ = 1 + (n − 1)3 = 1 + 3n − 3 = 3n − 2. Therefore option B is correct. Substitution verifies the rule: n = 1 gives 1, n = 2 gives 4, n = 3 gives 7, and n = 4 gives 10. Option A begins with 4, option C has common difference 1, and option D begins with 1 but has common difference 4, so none describes the complete sequence.
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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