If aₙ = n³ − n, what will be the value of a₇ − a₅?
Answer and explanation
Correct answer: 216
The governing concept is evaluation of an explicit, or general, rule for a sequence. Substitute n = 7 and n = 5 separately into aₙ = n³ − n. We get a₇ = 7³ − 7 = 343 − 7 = 336, and a₅ = 5³ − 5 = 125 − 5 = 120. Therefore, a₇ − a₅ = 336 − 120 = 216, so option B is correct. A useful algebraic check is 7³ − 7 − (5³ − 5) = 343 − 7 − 125 + 5 = 216. The other options arise from an incorrect cube, forgetting the subtraction of n, or subtracting the terms incorrectly. Evaluating each term carefully avoids those errors.
Frequently asked questions
What is the correct answer to this question?
216
Why is this the correct answer?
The governing concept is evaluation of an explicit, or general, rule for a sequence. Substitute n = 7 and n = 5 separately into aₙ = n³ − n. We get a₇ = 7³ − 7 = 343 − 7 = 336, and a₅ = 5³ − 5 = 125 − 5 = 120. Therefore, a₇ − a₅ = 336 − 120 = 216, so option B is correct. A useful algebraic check is 7³ − 7 − (5³ − 5) = 343 − 7 − 125 + 5 = 216. The other options arise from an incorrect cube, forgetting the subtraction of n, or subtracting the terms incorrectly. Evaluating each term carefully avoids those errors.
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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