Question

Find the sum to n terms of the sequence $8,88,888,\mathrm{8888....}$

Answer 1

We have,

$8,88,888,\mathrm{8888........}$

First term $a=8$

Common ratio $r=\frac{IIndterm}{Istterm}$

$r=\frac{88}{8}=11r>1$

Sum of n term is $=S_n=?$

$S_n=\frac{a(r^n-1)}{r-1}r>1$

$S_n=\frac{8({11}^r-1)}{11-1}$

$S_n=\frac{8({11}^r-1)}{10}$

Hence, this is the answer.