Math CentralQuandaries & Queries


Subject: Finding the Nth term
Name: Lisa
Who are you: Student

Hi, I am really stuck on this question, and I can't find the answer anywhere:


What is the nth term for the sequence, '1, 3, 6, 10...' and could you say how you got the anwser.
Thanks a lot,


Hi Lisa. Whenever I get these kinds of problems, one of my first strategies is to look at the differences between the terms and/or the ratios between them to see if there is a pattern.

Your sequence is 1, 3, 6, 10, ... and the differences are 2, 3, 4, ... so actually each term is the sum of all the counting numbers up to the term number. So the fifth term in the sequence would be the sum of all the numbers up to 5: 1+2+3+4+5 = 15. This means the nth term is the sum of all the numbers up to n: 1+2+...+(n-1)+n.

Stephen La Rocque.>


There is a compact way to write 1+2+...+(n-1)+n, do you know what it is?

This is a really neat sequence of numbers, they are called triangular numbers.

triangular numbers


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