Date: Mon, 9 Nov 1998 09:12:58 -0600 (CST) Subject: sequences Name: Ilia Who is asking: Student Level: All Question: What the formula and explonation for formula for next patterns: 1) 1, 4, 10, 20, 35, 56, 84,... 2) 0, 6, 30, 90, 210, 420,... Thanks! Hi Ilia One way to approach this type of problem is to take differences of successive terms to form a new sequence, then do the same for those until we come to a sequence of equal differences or to a pattern you recognize and can continue. For example if the given sequence is 0, 2, 8, 21, 44, 80 then this procedure yields a constant row of three 3's. Extending this row to a fourth 3 allows the previous rows to be extended to give 132 at the next term in the original sequence. ``` 0, 2, 8, 21, 44, 80, 132 +2 +6 +13 +23 +36 +52 +4 +7 +10 +13 +16 +3 +3 +3 +3 ``` For your sequence 1, 4, 10, 20, 35, 56, 84,... the first row of differences is 3, 6, 10, 15, 21, 28 You should recognize the pattern that and hence the next term in the row of differences is and thus the next term in your sequence is 84+36 = 120. The same technique will work for the second sequence. Here the first row of differences is a constant times some binomial coefficients. Cheers Penny Go to Math Central To return to the previous page use your browser's back button.