help with arithmetic and geometric sequences
i'm having a bit of a mental block here. i'm studying series for my exam next week and there's something i cant quite get. in an arithmetic progression each subsequent term has a common difference and a geometric progression has a common ratio, i'm absolutely fine with this. this is my problem, take the squares for example;
1, 4, 9, 16, 25, ... and so on.
i cant see what the common ratio is here. another example;
(1 × 2) + (2 × 5) + (3 × 8) + · · · to n.
i'm trying to write that one in sigma notation but i just cant see what the common ratio is, according to my notes it should be k(3k-1). is there process i can use to figure this out or am i just supposed to "see" the pattern? any help here would be great because when it comes to finding the sum of a geometric series i'm completely done in so thanks in advance.