Question

The 6th term is 22 and the common difference is 6. what is the 50th term

Answer 1

The general formula for an arithmetic sequence is: 
a(n) = a + d(n - 1) 

a : first term 
d : common difference (6) 
n : number of the term 

In your example, you are told the 6th term is 22. 
a(6) = a + 6(6 - 1) = 22 
a + 30 = 22 
a = 22 - 30 
a = -8 

So now you have the general formula: 
a(n) = -8 + 6(n - 1) 

If you like you can simplify it: 
a(n) = -8 + 6n - 6 
a(n) = 6n - 14 

Then you can plug in n = 50: 
a(50) = 6(50) - 14 
= 300 - 14 
= 286