Question

The nth term of the sequence 0.7, 0.77, 0.777........ is $\frac{7}{9}[1-(0.1{)}^n]$

• A. True
• B. False

Answer 1

The correct option is A True

$0.7,0.77,0.777,....\frac{7}{10},\frac{77}{100},\frac{777}{1000},....7\left(\frac{1}{10}\right),7(\frac{1}{10}+\frac{1}{100}),7(\frac{1}{10}+\frac{1}{100}+\frac{1}{1000}),...$

$n^{th}$term=$7(\frac{1}{10}+\frac{1}{100}+....\frac{1}{{10}^n})=7\left(\frac{\frac{1}{10}(1-\frac{1}{{10}^n})}{(1-\frac{1}{10})}\right)=\frac{7}{9}(1-\frac{1}{{10}^n})$

$n^{th}$term=$\frac{7}{9}(1-{\left(0.1\right)}^n)$