Let’s say we are still looking at the same sequence – 5, 9, 13, 17, … Much quicker than writing out 200 terms I’m sure you would agree! So in a matter of seconds we know that the 200 th term in the sequence is 801. With the nth term, you can get it instantly. If you had never heard of the nth term before, the only way you would know how to do this is to continue writing out the sequence until you get to the 200 th term… which would be time-consuming to say the least! So it is fairly easy to find the next few terms in the sequence.īut where the nth term becomes really useful is if I asked you to find the 200 th term in the sequence. You can clearly see here that the sequence we have generated is linear and goes up by 4 each time. So we know the sequence starts 5, 9, 13, 17. I can find the 2 nd, 3 rd and 4 th terms as well too. Therefore I know the first term in the sequence is 5. If I wanted to find the 1 st term in the sequence, I can do that using the nth term. So let’s say a sequence has nth term 4n + 1. The nth term is a formula in terms of n that will find any term in the sequence that you want. ![]() What is the nth term, and why is it useful?įirst of all, let me explain what the nth term of a sequence is. This is a relatively simple process, but is incredibly useful. To determine the next triangular number in a pictorial sequence, we add another row to the triangle that contains one more element than the previous row.Following on from the last blog on identifying different types of sequences, in this blog I will show you how to find the nth term of a linear sequence. These are sometimes known as polygonal numbers or figurate numbers. Triangular numbers were originally explored by the Pythagoreans who developed many relationships between different geometric shapes and numbers including triangular numbers, square numbers, pentagonal numbers (numbers represented within a regular pentagon) and hexagonal numbers (numbers represented within a regular hexagon). Carl Gauss and Pierre de Fermat are known for their work with number theory. ![]() Each new row of dots in the triangle contains one more dot than the row above, creating a triangular pattern. The number of dots within each triangle determines the value of the term. ![]() Triangular numbers can be represented using equilateral triangles. To determine the next triangular number in a numerical sequence, when given the sequence, we need to find the difference between the previous two terms and add one more than this value. ![]() The third triangular number is found by adding 3 to the previous one. The second triangular number is found by adding 2 to the previous one. The numbers form a sequence known as the triangular numbers. Triangular numbers are numbers that can be represented as a triangle.
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