In an arithmetic sequence, a₈ = 41 and the common difference is 5. What is its nth term?
Answer and explanation
Correct answer: 5n + 1
The governing concept is the arithmetic-progression formula aₙ = a₁ + (n − 1)d. Since a₈ = a₁ + 7d, substitute the given values: 41 = a₁ + 7 × 5 = a₁ + 35. Thus a₁ = 6. The general term is then aₙ = 6 + (n − 1)5 = 6 + 5n − 5 = 5n + 1. Therefore option B is correct, so the supplied answer A needs correction. Verification gives a₈ = 5 × 8 + 1 = 41. Option A gives 46 at n = 8, while options C and D give 36 and 75 respectively, so they fail the given condition.
Frequently asked questions
What is the correct answer to this question?
5n + 1
Why is this the correct answer?
The governing concept is the arithmetic-progression formula aₙ = a₁ + (n − 1)d. Since a₈ = a₁ + 7d, substitute the given values: 41 = a₁ + 7 × 5 = a₁ + 35. Thus a₁ = 6. The general term is then aₙ = 6 + (n − 1)5 = 6 + 5n − 5 = 5n + 1. Therefore option B is correct, so the supplied answer A needs correction. Verification gives a₈ = 5 × 8 + 1 = 41. Option A gives 46 at n = 8, while options C and D give 36 and 75 respectively, so they fail the given condition.
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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