What is the general term of the sequence (5/2, 5, 15/2, 10, …)?
Answer and explanation
Correct answer: aₙ = 5n/2
The sequence consists of consecutive multiples of 5/2. Substituting n = 1, 2, 3, and 4 into aₙ = 5n/2 gives 5/2, 10/2 = 5, 15/2, and 20/2 = 10, respectively. Therefore option A is correct. The arithmetic-sequence formula confirms this: the first term is 5/2 and the common difference is also 5/2, so aₙ = 5/2 + (n − 1)(5/2) = 5n/2. Option B gives 1/5 for the first term, option C gives 5, and option D gives 7, so none of those matches the first term and the subsequent pattern. The fraction should remain attached to n as the multiplier 5/2.
Frequently asked questions
What is the correct answer to this question?
aₙ = 5n/2
Why is this the correct answer?
The sequence consists of consecutive multiples of 5/2. Substituting n = 1, 2, 3, and 4 into aₙ = 5n/2 gives 5/2, 10/2 = 5, 15/2, and 20/2 = 10, respectively. Therefore option A is correct. The arithmetic-sequence formula confirms this: the first term is 5/2 and the common difference is also 5/2, so aₙ = 5/2 + (n − 1)(5/2) = 5n/2. Option B gives 1/5 for the first term, option C gives 5, and option D gives 7, so none of those matches the first term and the subsequent pattern. The fraction should remain attached to n as the multiplier 5/2.
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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