What is the general term of the sequence (8, 15, 22, 29, …)?
Answer and explanation
Correct answer: aₙ = 7n + 1
The difference between consecutive terms is constant: 15 − 8 = 7, 22 − 15 = 7, and 29 − 22 = 7. Thus this is an arithmetic sequence with first term a₁ = 8 and common difference d = 7. Applying aₙ = a₁ + (n − 1)d gives aₙ = 8 + 7(n − 1) = 8 + 7n − 7 = 7n + 1. Therefore option A is correct. Direct checking gives 7(1) + 1 = 8, 7(2) + 1 = 15, 7(3) + 1 = 22, and 7(4) + 1 = 29. Option C starts at 6, option B starts at 8 but then gives 16, and option D has difference 1 rather than 7.
Frequently asked questions
What is the correct answer to this question?
aₙ = 7n + 1
Why is this the correct answer?
The difference between consecutive terms is constant: 15 − 8 = 7, 22 − 15 = 7, and 29 − 22 = 7. Thus this is an arithmetic sequence with first term a₁ = 8 and common difference d = 7. Applying aₙ = a₁ + (n − 1)d gives aₙ = 8 + 7(n − 1) = 8 + 7n − 7 = 7n + 1. Therefore option A is correct. Direct checking gives 7(1) + 1 = 8, 7(2) + 1 = 15, 7(3) + 1 = 22, and 7(4) + 1 = 29. Option C starts at 6, option B starts at 8 but then gives 16, and option D has difference 1 rather than 7.
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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