If aₙ = 2n² + 5n − 3, what is the value of a₄ + a₂?
Answer and explanation
Correct answer: 54
The governing concept is evaluating multiple terms from an explicit quadratic sequence rule and then combining them. First calculate a₄ by substituting n = 4: a₄ = 2(4²) + 5(4) − 3 = 2(16) + 20 − 3 = 49. Next calculate a₂: a₂ = 2(2²) + 5(2) − 3 = 2(4) + 10 − 3 = 15, not 5. Therefore a₄ + a₂ = 49 + 15 = 64. Since 64 is not among the supplied options, the item is internally inconsistent and cannot have a valid unambiguous answer as written. The stated key B and its explanation are mathematically incorrect; option B would require a₂ = 5, which does not follow from the rule.
Frequently asked questions
What is the correct answer to this question?
54
Why is this the correct answer?
The governing concept is evaluating multiple terms from an explicit quadratic sequence rule and then combining them. First calculate a₄ by substituting n = 4: a₄ = 2(4²) + 5(4) − 3 = 2(16) + 20 − 3 = 49. Next calculate a₂: a₂ = 2(2²) + 5(2) − 3 = 2(4) + 10 − 3 = 15, not 5. Therefore a₄ + a₂ = 49 + 15 = 64. Since 64 is not among the supplied options, the item is internally inconsistent and cannot have a valid unambiguous answer as written. The stated key B and its explanation are mathematically incorrect; option B would require a₂ = 5, which does not follow from the rule.
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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