problem: A sequence starts with the term 2222. Each succeeding term is found by adding 1010 to the previous term. What is the sum of the sixth and seventh terms?
solution: The $n$th term of the sequence is $2222+1010(n-1)$.  Therefore, the sum of the sixth and seventh terms is $2222+1010(5)+2222+1010(6)=4444+1010(11)=4444+11110=\boxed{15554}$.