What is the simplified (n)th term of the sequence \(\frac{1}{3},\frac{4}{8},\frac{9}{15},\frac{16}{24},\ldots\)?
Answer and explanation
Correct answer: \(\frac{n}{n+2}\)
The numerators \(1,4,9,16\) are \(1^2,2^2,3^2,4^2\), so the numerator of the nth term is \(n^2\). The denominators \(3,8,15,24\) are respectively \(1(1+2),2(2+2),3(3+2),4(4+2)\). Hence, the denominator is \(n(n+2)\). Therefore, the nth term is \(\frac{n^2}{n(n+2)}=\frac{n}{n+2}\). Option B has the numerator pattern but not the required denominator. Exam tip: in fractional sequences, find the numerator and denominator patterns separately before simplifying.
Frequently asked questions
What is the correct answer to this question?
\(\frac{n}{n+2}\)
Why is this the correct answer?
The numerators \(1,4,9,16\) are \(1^2,2^2,3^2,4^2\), so the numerator of the nth term is \(n^2\). The denominators \(3,8,15,24\) are respectively \(1(1+2),2(2+2),3(3+2),4(4+2)\). Hence, the denominator is \(n(n+2)\). Therefore, the nth term is \(\frac{n^2}{n(n+2)}=\frac{n}{n+2}\). Option B has the numerator pattern but not the required denominator. Exam tip: in fractional sequences, find the numerator and denominator patterns separately before simplifying.
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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