To find out the equation for a sequence, the first thing you note is the difference between the numbers. In this case the difference is:
-8, -8, -8, -8
Thus the formula will be x-8n where x is not yet known.
For linear sequences like the one above, x is the 0th term. In this case it would be the term that would come before 22, or 22+8, or 30.
Thus the equation for the nth term is 30-8n
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The nth term is 3n+7 and so the next number will be 22
The sequence has a difference of 10, so the nth term starts with 10n. Then to get to -8 from 10 you need to subtract 18. So the nth term is 10n - 18.
6n+10
You must mean what is the next number in the series, not the 'nth', which is undefined. The next number is 58.
3n+7