Find the 12th term of the AP (1/3, 2/3, 1, 4/3, …).
Answer and explanation
Correct answer: 4
The governing concept is the nth-term formula for an arithmetic progression: aₙ = a + (n − 1)d. The first term is a = 1/3. The common difference is d = 2/3 − 1/3 = 1/3; the later terms confirm the same difference because 1 − 2/3 = 1/3. For n = 12, a₁₂ = 1/3 + (12 − 1)(1/3) = 1/3 + 11/3 = 12/3 = 4. Thus option D is correct. The multiplier is 11 rather than 12 because the first term is already present, and only eleven equal steps are needed to reach the twelfth term. The other options arise from counting the steps incorrectly or stopping at an earlier term.
Frequently asked questions
What is the correct answer to this question?
4
Why is this the correct answer?
The governing concept is the nth-term formula for an arithmetic progression: aₙ = a + (n − 1)d. The first term is a = 1/3. The common difference is d = 2/3 − 1/3 = 1/3; the later terms confirm the same difference because 1 − 2/3 = 1/3. For n = 12, a₁₂ = 1/3 + (12 − 1)(1/3) = 1/3 + 11/3 = 12/3 = 4. Thus option D is correct. The multiplier is 11 rather than 12 because the first term is already present, and only eleven equal steps are needed to reach the twelfth term. The other options arise from counting the steps incorrectly or stopping at an earlier term.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Arithmetic Progressions (AP). Topic: Finding the $n$th term of an AP.
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