Question

The sixth term is 22 and the common difference is six what is the fiftieth term

Answer 1

Hey! :)

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
So your answer is 286

Hope this helps! :)