If a_n = 13n - 8, what is a_9 - a_4?
Answer and explanation
Correct answer: 65
The governing concept is evaluating two terms from an explicit linear rule and then finding their difference. For n = 9, a_9 = 13(9) - 8 = 117 - 8 = 109. For n = 4, a_4 = 13(4) - 8 = 52 - 8 = 44. Therefore, a_9 - a_4 = 109 - 44 = 65, so option B is correct. There is also a useful shortcut: because the coefficient of n is 13, increasing the index from 4 to 9 by 5 increases the term by 5 × 13 = 65; the constant -8 cancels in the subtraction. Option A corresponds to only four index steps, while C and D overcount the change. Both direct calculation and the shortcut confirm 65.
Frequently asked questions
What is the correct answer to this question?
65
Why is this the correct answer?
The governing concept is evaluating two terms from an explicit linear rule and then finding their difference. For n = 9, a_9 = 13(9) - 8 = 117 - 8 = 109. For n = 4, a_4 = 13(4) - 8 = 52 - 8 = 44. Therefore, a_9 - a_4 = 109 - 44 = 65, so option B is correct. There is also a useful shortcut: because the coefficient of n is 13, increasing the index from 4 to 9 by 5 increases the term by 5 × 13 = 65; the constant -8 cancels in the subtraction. Option A corresponds to only four index steps, while C and D overcount the change. Both direct calculation and the shortcut confirm 65.
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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