Question

The sum of sequence $0.15,0.015,0.0015,.....$ upto 20 term is ?

• A. $\frac{1}{6}[1-(0.1{)}^{20}]$
• B. $\frac{1}{6}[1+(0.1{)}^{20}]$
• C. $\frac{1}{3}[1-(0.1{)}^{20}]$
• D. None of these

Answer 1

The correct option is A $\frac{1}{6}[1-(0.1{)}^{20}]$

Since the sequence is a GP with

$a=0.15;r=\frac{0.015}{0.15}=0.1;n=20\therefore S_n=\frac{a(1-r^n)}{(1-r)}=\frac{0.15(1-{\left(0.1\right)}^{20})}{1-0.1}=\frac{1}{6}(1-{\left(0.1\right)}^{20})$