In an arithmetic sequence, a₇ = 38 and the common difference is 6. What is its nth term?
Answer and explanation
Correct answer: 6n − 4
The governing concept is the nth-term formula for an arithmetic progression: aₙ = a₁ + (n − 1)d. Since a₇ = a₁ + 6d and d = 6, we get 38 = a₁ + 36, so a₁ = 2. Therefore aₙ = 2 + (n − 1)6 = 2 + 6n − 6 = 6n − 4. Thus option B is correct. A quick check confirms it: substituting n = 7 gives 42 − 4 = 38, exactly as required. Option A has the wrong constant term and gives 44 at n = 7; option C gives 50; option D incorrectly uses 7 as the coefficient of n rather than the common difference 6.
Frequently asked questions
What is the correct answer to this question?
6n − 4
Why is this the correct answer?
The governing concept is the nth-term formula for an arithmetic progression: aₙ = a₁ + (n − 1)d. Since a₇ = a₁ + 6d and d = 6, we get 38 = a₁ + 36, so a₁ = 2. Therefore aₙ = 2 + (n − 1)6 = 2 + 6n − 6 = 6n − 4. Thus option B is correct. A quick check confirms it: substituting n = 7 gives 42 − 4 = 38, exactly as required. Option A has the wrong constant term and gives 44 at n = 7; option C gives 50; option D incorrectly uses 7 as the coefficient of n rather than the common difference 6.
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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