What is the general term of the sequence (4, 7, 10, 13, …)?
Answer and explanation
Correct answer: a_n = 3n + 1
The governing concept is the explicit formula for an arithmetic sequence. The terms increase by a constant common difference, d = 7 − 4 = 3. For an arithmetic sequence, a_n = a_1 + (n − 1)d. Substituting a_1 = 4 and d = 3 gives a_n = 4 + 3(n − 1) = 4 + 3n − 3 = 3n + 1. Checking n = 1 gives 4, n = 2 gives 7, and n = 3 gives 10, so option A matches every listed term. Option B gives 4, 8, 12, while option C starts with 2 and option D gives 4, 5, 6; therefore they do not describe the sequence.
Frequently asked questions
What is the correct answer to this question?
a_n = 3n + 1
Why is this the correct answer?
The governing concept is the explicit formula for an arithmetic sequence. The terms increase by a constant common difference, d = 7 − 4 = 3. For an arithmetic sequence, a_n = a_1 + (n − 1)d. Substituting a_1 = 4 and d = 3 gives a_n = 4 + 3(n − 1) = 4 + 3n − 3 = 3n + 1. Checking n = 1 gives 4, n = 2 gives 7, and n = 3 gives 10, so option A matches every listed term. Option B gives 4, 8, 12, while option C starts with 2 and option D gives 4, 5, 6; therefore they do not describe the sequence.
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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