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

A. $5\left(10^{n}-1\right)$ B. $5^{n}\left(10^{n}-1\right)$ C. $\frac{5}{9} \times\left(10^{n}-1\right)$ D. $\left(\frac{5}{9}\right)^{n} \times\left(10^{n}-1\right)$ Answer: Option C
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Solution(By Apex Team)

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

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