I have always taight zero term method for linear and incorporated that into quadratic but having read your notes, I am going to teach them your way today. (-1) in your explanation of the quadratic sequence (bottom line). The next three terms are: \(24 \times 2 = 48\), \(48 \times 2 = 96\) and \(96 \times 2 = 192\). GCSE Term-to-term sequences & Arithmetic vs Geometric Progressions. 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. ![]() 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
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