Question 739087
1. The common difference (slope) is equal to {{{(62 - 22)/(15 - 5) = 4}}}.
   The nth term is 4n + k, we solve for k by substituting n = 5 (and equate to 5th term).
   4(5) + k = 22 so k = 2. 
   The nth term is 4n + 2.
   The 100th term is 4(100) + 2 = {{{highlight(402)}}}.
2. The sum of the first n positive integers is equal to {{{n(n+1)/2}}} and the  sum of the first n even positive integers is {{{n(n+1)}}}.
   Therefore, the sum of the first 50 positive even integers is {{{50(51) =  highlight(2550)}}}.