GRE Pattern changing?

Sequence/pattern with a changing difference?(corrected)?

• ~i am re-posting this question because the original post has some really bad errors on my part (i deleted the original) i dont know if the pattern would be called a sequence. im trying to find a certain number in the sequence/pattern. i find that with every number in the sequence the difference is 4 more then the previous difference. that is, if d is the difference between two consecutive numbers in the sequence then d1 = 4, d2 = 8, d3 = 12, d4 = 16, and so on the sequence im looking at is 4, 12, 24, 40....... (if there any mistake refer to this part than the written part above) is there a systematic way of finding a specific number in the sequence/pattern?

• Answer:

  Yes, you can get it by finding difference of neighbor terms. Original: .......4, 12, 24, 40 Difference:......8, 12, 16 Therefore, t(n) = 4+8+12+16+...+4n = 4(1+2+...+n) = 2(1+n)n = 2n^2 + 2n Check: t(1) = 2+2 = 4, t(2) = 2*4+2*2 = 12,.... So, it works.