Sequence DifferencesDate: 06/24/2003 at 16:22:38 From: Anthony Subject: Problem solving The third and fourth terms of a sequence are 26 and 40. If the second differences are a constant 4, what are the first five terms of the sequence? Date: 06/25/2003 at 08:20:22 From: Doctor Edwin Subject: Re: Problem solving Hi, Anthony. I'm not sure where your difficulty is. Is it that you don't know what "second differences" means, or that you don't know how to apply it to this problem? Let's talk about the terminology for a minute. "First difference" is the difference between the numbers in the series. The series itself looks like: ? ? 26 40 ? That is, we know two out of the five terms. So what's the first difference between the third and fourth terms? 14 -- first difference / \ ? ? 26 40 ? -- series Now the second difference is the difference between the first differences. They've told us that it's 4 for all the terms: 4 4 4 -- second difference / \ / \ / \ ? ? 14 ? -- first difference / \ / \ / \ / \ ? ? 26 40 ? -- series So what's the last first difference in our picture? It's going to be 4 more than the one before it, or 18: 4 4 4 -- second difference / \ / \ / \ ? ? 14 18 -- first difference / \ / \ / \ / \ ? ? 26 40 ? -- series Which means that the last number in the series is 18 more than the one before it. Is that enough to get you started? Write back if you need more help. - Doctor Edwin, The Math Forum http://mathforum.org/dr.math/ |
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