Which is the (n)th term of the sequence \(\frac{2}{9},\frac{5}{16},\frac{8}{23},\frac{11}{30},\ldots\)?
Answer and explanation
Correct answer: \(\frac{3n-1}{7n+2}\)
The numerators \(2,5,8,11,\ldots\) form an arithmetic progression whose nth term is \(2+(n-1)\times3=3n-1\). The denominators \(9,16,23,30,\ldots\) also form an arithmetic progression whose nth term is \(9+(n-1)\times7=7n+2\). Hence, the nth term is \(\frac{3n-1}{7n+2}\). Option D has the correct numerator, but for \(n=1\) its denominator is 10 instead of 9. Exam tip: in a sequence of fractions, identify the numerator and denominator patterns separately.
Frequently asked questions
What is the correct answer to this question?
\(\frac{3n-1}{7n+2}\)
Why is this the correct answer?
The numerators \(2,5,8,11,\ldots\) form an arithmetic progression whose nth term is \(2+(n-1)\times3=3n-1\). The denominators \(9,16,23,30,\ldots\) also form an arithmetic progression whose nth term is \(9+(n-1)\times7=7n+2\). Hence, the nth term is \(\frac{3n-1}{7n+2}\). Option D has the correct numerator, but for \(n=1\) its denominator is 10 instead of 9. Exam tip: in a sequence of fractions, identify 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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