What is the nth term of the sequence 3/2, 5/3, 7/4, 9/5, …?
Answer and explanation
Correct answer: (2n + 1)/(n + 1)
The governing concept is forming a general rule for a sequence of fractions by finding separate numerator and denominator patterns. The numerators are 3, 5, 7, 9, which follow 2n + 1 when n starts at 1. The denominators are 2, 3, 4, 5, which follow n + 1. Combining these independent patterns gives aₙ = (2n + 1)/(n + 1). Substitution confirms it: n = 1 gives 3/2, n = 2 gives 5/3, and n = 4 gives 9/5. Option B starts with 1/2, option C reverses the structure, and option D gives 3 rather than 3/2 for n = 1.
Frequently asked questions
What is the correct answer to this question?
(2n + 1)/(n + 1)
Why is this the correct answer?
The governing concept is forming a general rule for a sequence of fractions by finding separate numerator and denominator patterns. The numerators are 3, 5, 7, 9, which follow 2n + 1 when n starts at 1. The denominators are 2, 3, 4, 5, which follow n + 1. Combining these independent patterns gives aₙ = (2n + 1)/(n + 1). Substitution confirms it: n = 1 gives 3/2, n = 2 gives 5/3, and n = 4 gives 9/5. Option B starts with 1/2, option C reverses the structure, and option D gives 3 rather than 3/2 for n = 1.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Sequences and Progressions. Topic: nth term.
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