If aₙ = 4n² + 7n, what is the value of a₈ − a₃?
Answer and explanation
Correct answer: 255
The governing concept is evaluating an explicit sequence rule at two specified indices and then subtracting. First calculate a₈: a₈ = 4(8²) + 7(8) = 4(64) + 56 = 256 + 56 = 312. Next calculate a₃: a₃ = 4(3²) + 7(3) = 4(9) + 21 = 36 + 21 = 57. Therefore, a₈ − a₃ = 312 − 57 = 255, so option B is correct. Option A, C, and D can result from arithmetic slips such as miscalculating one square, multiplying incorrectly, or subtracting inaccurately. The original answer marking was corrected because 255, not 265, follows from the stated rule.
Frequently asked questions
What is the correct answer to this question?
255
Why is this the correct answer?
The governing concept is evaluating an explicit sequence rule at two specified indices and then subtracting. First calculate a₈: a₈ = 4(8²) + 7(8) = 4(64) + 56 = 256 + 56 = 312. Next calculate a₃: a₃ = 4(3²) + 7(3) = 4(9) + 21 = 36 + 21 = 57. Therefore, a₈ − a₃ = 312 − 57 = 255, so option B is correct. Option A, C, and D can result from arithmetic slips such as miscalculating one square, multiplying incorrectly, or subtracting inaccurately. The original answer marking was corrected because 255, not 265, follows from the stated rule.
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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