Find the nth term of the following sequence : 5 + 55 + 555 + . . . . Tn

Answer: Option C

We will it through option checking method:
$$\begin{array}{rl}& \frac{5}{9}\times \left({10}^n-1\right)\\ & \text{We}\text{put}n=1,\\ & \frac{5}{9}\times \left({10}^1-1\right)=5\\ & n=2\left(\frac{5}{9}\right)\times \left({10}^2-1\right)=55\\ & n=3\left(\frac{5}{9}\right)\times \left({10}^3-1\right)=555\end{array}$$
It means Option C is satisfying the sequence so the n^th term would be
$$\frac{5}{9}\times \left({10}^n-1\right)$$