If a_n = n³ + n², what will be the value of a_6 − a_4?
Answer and explanation
Correct answer: 172
The governing concept is evaluation of an explicit nth-term formula, including both the cube and the square of the index. For n = 6, substitute carefully: a₆ = 6³ + 6² = 216 + 36 = 252. For n = 4, a₄ = 4³ + 4² = 64 + 16 = 80. Hence a₆ − a₄ = 252 − 80 = 172, making option C correct. The two terms should be calculated separately before subtraction. Omitting the square or cube, using an incorrect power, or making an arithmetic error in the final subtraction can produce distractors such as 162, 168, or 176. Since the formula contains a sum of two powers, both components must be included for each index.
Frequently asked questions
What is the correct answer to this question?
172
Why is this the correct answer?
The governing concept is evaluation of an explicit nth-term formula, including both the cube and the square of the index. For n = 6, substitute carefully: a₆ = 6³ + 6² = 216 + 36 = 252. For n = 4, a₄ = 4³ + 4² = 64 + 16 = 80. Hence a₆ − a₄ = 252 − 80 = 172, making option C correct. The two terms should be calculated separately before subtraction. Omitting the square or cube, using an incorrect power, or making an arithmetic error in the final subtraction can produce distractors such as 162, 168, or 176. Since the formula contains a sum of two powers, both components must be included for each index.
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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