Find the 12th term of the AP (13, 23, 33, 43, …).
Answer and explanation
Correct answer: 123
The governing concept is the nth-term formula of an arithmetic progression. The first term is a = 13, and the common difference is d = 23 − 13 = 10; the sequence increases by 10 each time. Thus a_12 = a + (12 − 1)d = 13 + 11 × 10 = 13 + 110 = 123. Therefore option B is correct. The multiplier is 11 because eleven equal gaps separate the first and twelfth terms. Option A could arise from subtracting or miscounting one step, while options C and D use twelve or more increments rather than the required eleven. The calculation also confirms the pattern: the terms are 10k + 3 for k = 1, 2, …, so the twelfth is 120 + 3 = 123.
Frequently asked questions
What is the correct answer to this question?
123
Why is this the correct answer?
The governing concept is the nth-term formula of an arithmetic progression. The first term is a = 13, and the common difference is d = 23 − 13 = 10; the sequence increases by 10 each time. Thus a_12 = a + (12 − 1)d = 13 + 11 × 10 = 13 + 110 = 123. Therefore option B is correct. The multiplier is 11 because eleven equal gaps separate the first and twelfth terms. Option A could arise from subtracting or miscounting one step, while options C and D use twelve or more increments rather than the required eleven. The calculation also confirms the pattern: the terms are 10k + 3 for k = 1, 2, …, so the twelfth is 120 + 3 = 123.
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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