Nth Term in a SequenceDate: 01/11/2003 at 12:41:35 From: Xina Subject: Sequence and series Here is the sequence: 1, 2, 5, 14 ... Find the following 2 terms and a formula for the nth term. Are we expected to use trial and error to find the nth term, or are there any nice formulas to help us? Date: 01/12/2003 at 00:15:37 From: Doctor Kastner Subject: Re: Sequence and series Hi Xina - Sadly, there are no nice formulas that you can use to figure out these sorts of problems. All is not lost, however; we just need to expand our thinking a bit. Looking for a common difference is a good first start, but what we really want to find is some type of pattern. Let's think about the following sequence: 1 3 6 10 15 If you look at the differences between terms, you'll see that it goes 2 3 4 5 So while there isn't a common difference, there is a clear pattern to the differences, and the next numbers would be 21 and 28. The same is true for the sequence 1 2 4 8 16 32 The differences are 1 2 4 8 16 which again doesn't have a common term, but it is a nice pattern of doubling. With this in mind, let's look back at your sequence. The differences are 1 3 9 which again suggests a pattern. Do you see the next number? I hope this helps. Write back if you're still stuck, or if you have other questions. - Doctor Kastner, The Math Forum http://mathforum.org/dr.math/ |
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