In an arithmetic sequence, a₉ = 61 and the common difference is 7. What is its nth term?
Answer and explanation
Correct answer: 7n − 2
The governing concept is the nth-term formula for an arithmetic progression: aₙ = a₁ + (n − 1)d. Since the ninth term is 61 and the common difference is 7, move backward eight common differences to obtain the first term: a₁ = 61 − 8(7) = 61 − 56 = 5. Therefore, aₙ = 5 + (n − 1)7 = 5 + 7n − 7 = 7n − 2. Substitution of n = 9 gives 63 − 2 = 61, confirming the result. Option B incorrectly uses a different constant, option C shifts it still further, and option D has the wrong coefficient of n.
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What is the correct answer to this question?
7n − 2
Why is this the correct answer?
The governing concept is the nth-term formula for an arithmetic progression: aₙ = a₁ + (n − 1)d. Since the ninth term is 61 and the common difference is 7, move backward eight common differences to obtain the first term: a₁ = 61 − 8(7) = 61 − 56 = 5. Therefore, aₙ = 5 + (n − 1)7 = 5 + 7n − 7 = 7n − 2. Substitution of n = 9 gives 63 − 2 = 61, confirming the result. Option B incorrectly uses a different constant, option C shifts it still further, and option D has the wrong coefficient of n.
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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