If aₙ = 9n − 4, what is a₈ − a₃?
Answer and explanation
Correct answer: 45
The governing concept is substitution into an explicit sequence rule, followed by subtraction of two terms. For the eighth term, substitute n = 8: a₈ = 9(8) − 4 = 72 − 4 = 68. For the third term, substitute n = 3: a₃ = 9(3) − 4 = 27 − 4 = 23. Therefore a₈ − a₃ = 68 − 23 = 45, so option B is correct. A useful shortcut is that the constant term cancels: (9 × 8 − 4) − (9 × 3 − 4) = 9(8 − 3) = 45. Option A could result from an arithmetic error, while options C and D do not follow from the required evaluations. Both terms must be calculated using their correct indices before finding the difference.
Frequently asked questions
What is the correct answer to this question?
45
Why is this the correct answer?
The governing concept is substitution into an explicit sequence rule, followed by subtraction of two terms. For the eighth term, substitute n = 8: a₈ = 9(8) − 4 = 72 − 4 = 68. For the third term, substitute n = 3: a₃ = 9(3) − 4 = 27 − 4 = 23. Therefore a₈ − a₃ = 68 − 23 = 45, so option B is correct. A useful shortcut is that the constant term cancels: (9 × 8 − 4) − (9 × 3 − 4) = 9(8 − 3) = 45. Option A could result from an arithmetic error, while options C and D do not follow from the required evaluations. Both terms must be calculated using their correct indices before finding the difference.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Sequences and Progressions. Topic: Explicit or general rule.
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