Which general term is correct for the sequence 5/2, 9, 39/2, 34, …?
Answer and explanation
Correct answer: aₙ = n(4n + 1)/2
The governing concept is an explicit rule: a formula must produce the term directly from its position n. Test option A at the first four positive integer values. For n = 1, a₁ = 1(4 + 1)/2 = 5/2. For n = 2, a₂ = 2(8 + 1)/2 = 9. For n = 3, a₃ = 3(12 + 1)/2 = 39/2, and for n = 4, a₄ = 4(16 + 1)/2 = 34. Thus option A reproduces every listed term. Option B gives 5/2 for the first term but fails at n = 2, option C gives 3, and option D gives 2 at n = 1, so they cannot be correct.
Frequently asked questions
What is the correct answer to this question?
aₙ = n(4n + 1)/2
Why is this the correct answer?
The governing concept is an explicit rule: a formula must produce the term directly from its position n. Test option A at the first four positive integer values. For n = 1, a₁ = 1(4 + 1)/2 = 5/2. For n = 2, a₂ = 2(8 + 1)/2 = 9. For n = 3, a₃ = 3(12 + 1)/2 = 39/2, and for n = 4, a₄ = 4(16 + 1)/2 = 34. Thus option A reproduces every listed term. Option B gives 5/2 for the first term but fails at n = 2, option C gives 3, and option D gives 2 at n = 1, so they cannot be correct.
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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