What is the next term in the pattern: 0.2, 0.22, 0.222?

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What is the next term in the pattern: 0.2, 0.22, 0.222?

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Answer 1 · 2018-06-05T11:27:03

Obviously $0.2222$ $0.2222$

Explanation:

Observe how numbers in sequence are constructed

$0.2 = \frac{2}{10}$ $0.2=2/10$ (1 term)
$0.22 = 0.2 + 0.02 = \frac{2}{10} + \frac{2}{100}$ $0.22=0.2+0.02=2/10+2/100$ (two terms)
$0.222 = 0.2 + 0.02 + 0.002 = \frac{2}{10} + \frac{2}{100} + \frac{2}{1000}$ $0.222=0.2+0.02+0.002=2/10+2/100+2/1000$ (three terms)

fourth term must be $0.2222 = \frac{2}{10} + \frac{2}{100} + \frac{2}{1000} + \frac{2}{10000}$ $0.2222=2/10+2/100+2/1000+2/10000$

With this patern the $n^{t h}$ $n^(th)$ term

$0.2222...^(nterms)...22=2/10+2/10^2+2/10^3+...+2/10^n$

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What is the next term in the pattern: 0.2, 0.22, 0.222?

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