Discussion
The general term of a sequence is \(t_{n} = \dfrac{n(n + 6)}{n + 4}\) ,n= \(1, 2, 3, ....\) If \(t_{n} = 5\), then the value of \(n\) is
Answer: C
\(n = \) 4.
Set the general term equal to 5 and clear the denominator:
\[ \begin{aligned} n(n + 6) &= 5(n + 4) \\ n^{2} + n - 20 &= 0 \\ (n + 5)(n - 4) &= 0 \end{aligned} \]
Since \(n\) is a natural number, \(n = 4\). Check: \(t_{4} = \frac{4 \times 10}{8} = 5\). For the other options, \(t_{2} = \frac{16}{6}\), \(t_{3} = \frac{27}{7}\), \(t_{5} = \frac{55}{9}\) and \(t_{6} = \frac{72}{10}\), none equal to 5.
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