Question

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

Answer 1

Obviously `0.2222`

Explanation:

Observe how numbers in sequence are constructed

`0.2=2/10` (1 term)
`0.22=0.2+0.02=2/10+2/100` (two terms)
`0.222=0.2+0.02+0.002=2/10+2/100+2/1000` (three terms)

fourth term must be `0.2222=2/10+2/100+2/1000+2/10000`

With this patern the `n^(th)` term

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