What is the general term of the arithmetic progression (7, 12, 17, 22, …)?
Answer and explanation
Correct answer: aₙ = 5n + 2
The governing concept is the nth-term formula for an arithmetic progression: aₙ = a₁ + (n − 1)d. Here the first term is a₁ = 7 and the common difference is d = 12 − 7 = 5. Therefore, aₙ = 7 + (n − 1)5 = 7 + 5n − 5 = 5n + 2. A useful check is to substitute n = 1: 5(1) + 2 = 7, and n = 2 gives 12, so the formula matches the sequence. Option A incorrectly treats 7 as the coefficient of n, option C gives a first term of 3, and option D gives a first term of 7 but has common difference 2 rather than 5. Hence option B is correct.
Frequently asked questions
What is the correct answer to this question?
aₙ = 5n + 2
Why is this the correct answer?
The governing concept is the nth-term formula for an arithmetic progression: aₙ = a₁ + (n − 1)d. Here the first term is a₁ = 7 and the common difference is d = 12 − 7 = 5. Therefore, aₙ = 7 + (n − 1)5 = 7 + 5n − 5 = 5n + 2. A useful check is to substitute n = 1: 5(1) + 2 = 7, and n = 2 gives 12, so the formula matches the sequence. Option A incorrectly treats 7 as the coefficient of n, option C gives a first term of 3, and option D gives a first term of 7 but has common difference 2 rather than 5. Hence option B is correct.
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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