Millionth Term of a SequenceDate: 06/18/2002 at 19:16:06 From: Lisa Vinson Subject: word problem w/ sequence What would be the millionth term in the sequence 1,2,2,3,3,3,4,4,4,4,...? I don't know where to start!! Date: 06/18/2002 at 20:41:25 From: Doctor Ian Subject: Re: word problem w/ sequence Hi Lisa, We can arrange the sequence this way: 1 2 2 3 3 3 4 4 4 4 5 5 5 5 5 6 6 6 6 6 6 How does that help? Well, let's look at the cumulative number of terms as a function of row number: 1 1 term total 2 2 3 3 3 3 6 4 4 4 4 10 5 5 5 5 5 15 6 6 6 6 6 6 21 The numbers in the column to the right are called 'triangular numbers', and there is a formula for finding the nth triangular number: n(n + 1) nth triangular number = -------- 2 (Check it against the numbers 1, 3, 6, 10, 15, and 21.) So what you want to know is: What is the smallest triangular number that is less than a million? Do you see why? Does this help? - Doctor Ian, The Math Forum http://mathforum.org/dr.math/ |
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