If aₙ = 6n² − 5n + 2, what is a₄ : a₂?
Answer and explanation
Correct answer: 39 : 8
The governing concept is substitution into an explicit rule followed by simplification of a ratio. For n = 4, a₄ = 6(4²) − 5(4) + 2 = 96 − 20 + 2 = 78. For n = 2, a₂ = 6(2²) − 5(2) + 2 = 24 − 10 + 2 = 16. Hence a₄ : a₂ = 78 : 16. Both terms are divisible by 2, so the simplest form is 39 : 8, making option B correct. Option A is the unsimplified ratio, while C and D result from incorrect substitution or arithmetic.
Frequently asked questions
What is the correct answer to this question?
39 : 8
Why is this the correct answer?
The governing concept is substitution into an explicit rule followed by simplification of a ratio. For n = 4, a₄ = 6(4²) − 5(4) + 2 = 96 − 20 + 2 = 78. For n = 2, a₂ = 6(2²) − 5(2) + 2 = 24 − 10 + 2 = 16. Hence a₄ : a₂ = 78 : 16. Both terms are divisible by 2, so the simplest form is 39 : 8, making option B correct. Option A is the unsimplified ratio, while C and D result from incorrect substitution or arithmetic.
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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