If aₙ = 6n² − n + 4, what is a₄ : a₂?
Answer and explanation
Correct answer: 48 : 13
The governing concept is evaluating an explicit formula and then simplifying a ratio. First calculate a₄: 6(4²) − 4 + 4 = 6·16 = 96. Next calculate a₂: 6(2²) − 2 + 4 = 24 − 2 + 4 = 26. Hence a₄ : a₂ = 96 : 26. Both numbers are divisible by 2, so the ratio in simplest form is 48 : 13, making option B correct. Option A is the correct unsimplified ratio, but the question asks for the ratio and the simplified option is preferred. Option C reverses the order, while option D uses an incorrect value for a₄.
Frequently asked questions
What is the correct answer to this question?
48 : 13
Why is this the correct answer?
The governing concept is evaluating an explicit formula and then simplifying a ratio. First calculate a₄: 6(4²) − 4 + 4 = 6·16 = 96. Next calculate a₂: 6(2²) − 2 + 4 = 24 − 2 + 4 = 26. Hence a₄ : a₂ = 96 : 26. Both numbers are divisible by 2, so the ratio in simplest form is 48 : 13, making option B correct. Option A is the correct unsimplified ratio, but the question asks for the ratio and the simplified option is preferred. Option C reverses the order, while option D uses an incorrect value for a₄.
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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