What is the eighth term of the arithmetic progression (42,36,30,24,\ldots)?
Answer and explanation
Correct answer: (0)
The governing concept is the nth-term formula for an arithmetic progression: a_n = a + (n - 1)d. In the sequence 42, 36, 30, 24, each term decreases by 6, so the first term is a = 42 and the common difference is d = -6. For the eighth term, substitute n = 8: a_8 = 42 + (8 - 1)(-6) = 42 + 7(-6) = 42 - 42 = 0. Therefore option D is correct. Option A is only the common difference, option B reverses its sign, and option C does not follow the repeated subtraction pattern.
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Why is this the correct answer?
The governing concept is the nth-term formula for an arithmetic progression: a_n = a + (n - 1)d. In the sequence 42, 36, 30, 24, each term decreases by 6, so the first term is a = 42 and the common difference is d = -6. For the eighth term, substitute n = 8: a_8 = 42 + (8 - 1)(-6) = 42 + 7(-6) = 42 - 42 = 0. Therefore option D is correct. Option A is only the common difference, option B reverses its sign, and option C does not follow the repeated subtraction pattern.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Sequences and Progressions. Topic: Arithmetic Progression.
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