![]() Show that the sequence 3, 6, 12, 24, … is a geometric sequence, and find the next three terms. This value is called the common ratio, r, which can be worked out by dividing one term by the previous term. In a geometric sequence, the term to term rule is to multiply or divide by the same value. The sequence will contain \(2n^2\), so use this: \ The coefficient of \(n^2\) is half the second difference, which is 2. Students are also required to recognise and use sequences of triangular, square and cube numbers, simple arithmetic. ![]() The second difference is the same so the sequence is quadratic and will contain an \(n^2\) term. This resource list is designed to provide an opportunity for students to make and test conjectures about recursive and long-term behaviour of geometric, quadratic and other sequences that arise within and outside mathematics. Work out the nth term of the sequence 5, 11, 21, 35. In this example, you need to add \(1\) to \(n^2\) to match the sequence. To work out the nth term of the sequence, write out the numbers in the sequence \(n^2\) and compare this sequence with the sequence in the question. understand the definition of a sequence, understand the domain and range of a sequence, classify a sequence as finite or infinite, understand how to classify a sequence as arithmetic, geometric, or neither, represent arithmetic and geometric sequences on a graph, generate sequences from graphs or diagrams. Half of 2 is 1, so the coefficient of \(n^2\) is 1. In this example, the second difference is 2. The coefficient of \(n^2\) is always half of the second difference. The sequence is quadratic and will contain an \(n^2\) term. Screens 1) Differentiate between the four major types of sequences (number patterns). The first differences are not the same, so work out the second differences. Work out the first differences between the terms. Work out the nth term of the sequence 2, 5, 10, 17, 26. They can be identified by the fact that the differences in-between the terms are not equal, but the second differences between terms are equal. Quadratic sequences are sequences that include an \(n^2\) term. Finding the nth term of quadratic sequences - Higher
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |