![]() ![]() For example, all of the following are quadratic sequences: 3, 6, 10, 15, 21, 7, 17, 31, 49, 71, 31, 30, 27, 22, 15, Quadratic sequences are related to squared numbers because each sequence includes a squared number an 2. 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. What is a Quadratic Sequence A quadratic sequence has the general form T (n) an2 + bn + c. 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. A quadratic sequence is a sequence of numbers in which the second difference between any two consecutive terms is constant. 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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