The general formula for an arithmetic sequence is: <span>a(n) = a + d(n - 1) </span>
<span>a : first term </span> <span>d : common difference (6) </span> <span>n : number of the term </span>
<span>In your example, you are told the 6th term is 22. </span> <span>a(6) = a + 6(6 - 1) = 22 </span> <span>a + 30 = 22 </span> <span>a = 22 - 30 </span> <span>a = -8 </span>
<span>So now you have the general formula: </span> <span>a(n) = -8 + 6(n - 1) </span>
<span>If you like you can simplify it: </span> <span>a(n) = -8 + 6n - 6 </span> <span>a(n) = 6n - 14 </span>
<span>Then you can plug in n = 50: </span> <span>a(50) = 6(50) - 14 </span> <span>= 300 - 14 </span> <span>= 286</span>