![]() ![]() So the common ratio is 2 and this is therefore a geometric sequence. Show that the sequence 3, 6, 12, 24, … is a geometric sequence, and find the next three terms.ĭividing each term by the previous term gives the same value: \(6 \div 3 = 12 \div 6 = 24 \div 12 = 2\). 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. The second difference is the same so the sequence is quadratic and will contain an \(n^2\) term. 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. 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. The first differences are not the same, so work out the second differences. 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. Work out the first differences between the terms. What is a Quadratic Sequence A quadratic sequence has the general form T(n) an 2 + bn + c. 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 |