8/16/2023 0 Comments Nth term of a sequence formulaShow 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. You can use it to find any property of the sequence the first term, common difference, n term, or the sum of the first n terms. The sequence will contain \(2n^2\), so use this: \ This arithmetic sequence calculator (also called the arithmetic series calculator) is a handy tool for analyzing a sequence of numbers that is created by adding a constant value each time. Substitute 24 for a 2 and 3 for a 5 in the formula a n a 1. The coefficient of \(n^2\) is half the second difference, which is 2. Given a geometric sequence with the first term a1 and the common ratio r, the nth (or general) term is given by. 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. So let’s say a sequence has nth term 4n 1. First find the common difference between each term and the next. The nth term is a formula in terms of n that will find any term in the sequence that you want. In this example, you need to add \(1\) to \(n^2\) to match the sequence. Find the n th term for this sequence: 1, 4, 7, 10. 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. Therefore, this sequence can be expressed by this general formula: To double check your formula and ensure that the answers work, plug in 1, 2, 3, and so on to make sure you get the original numbers from the given sequence. The sequence is quadratic and will contain an \(n^2\) term. This sequence is described by an 2 n 1. 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. The th term refers to a terms position in the sequence, for example, the first term has 1, the second term has 2 and so on. Finding the nth term of quadratic sequences - Higher
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