Which is the (n)th term of the sequence \(\frac{2}{5},\frac{5}{8},\frac{8}{11},\frac{11}{14},\ldots\)?
Answer and explanation
Correct answer: \(\frac{3n-1}{3n+2}\)
The numerators \(2,5,8,11,\ldots\) form an arithmetic progression with nth term \(2+(n-1)\times3=3n-1\). The denominators \(5,8,11,14,\ldots\) similarly have nth term \(5+(n-1)\times3=3n+2\). Therefore, the nth term of the given sequence is \(\frac{3n-1}{3n+2}\). For example, option D gives \(\frac{2}{4}\) at \(n=1\), not the first term \(\frac{2}{5}\). Exam tip: in fractional sequences, determine the numerator and denominator patterns separately.
Frequently asked questions
What is the correct answer to this question?
\(\frac{3n-1}{3n+2}\)
Why is this the correct answer?
The numerators \(2,5,8,11,\ldots\) form an arithmetic progression with nth term \(2+(n-1)\times3=3n-1\). The denominators \(5,8,11,14,\ldots\) similarly have nth term \(5+(n-1)\times3=3n+2\). Therefore, the nth term of the given sequence is \(\frac{3n-1}{3n+2}\). For example, option D gives \(\frac{2}{4}\) at \(n=1\), not the first term \(\frac{2}{5}\). Exam tip: in fractional sequences, determine the numerator and denominator patterns separately.
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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