###
**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**

## Show Answer

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
$\begin{aligned}\frac{5}{9}\times\left(10^n-1\right)\end{aligned}$

## Related Questions On Progressions

### How many terms are there in 20, 25, 30 . . . . . . 140?

A. 22B. 25

C. 23

D. 24

### Find the first term of an AP whose 8th and 12th terms are respectively 39 and 59.

A. 5B. 6

C. 4

D. 3

### Find the 15th term of the sequence 20, 15, 10 . . .

A. -45B. -55

C. -50

D. 0

### The sum of the first 16 terms of an AP whose first term and third term are 5 and 15 respectively is

A. 600B. 765

C. 640

D. 680