Geometric sequence formula nth term8/1/2023 The sum of the first n terms of a geometric progression is: The nth term of a geometric progression, where a is the first term and r is the common ratio, is:įor example, in the following geometric progression, the first term is 1, and the common ratio is 2: r is known as the common ratio of the sequence. the first 20 odd numbers).Ī geometric progression is a sequence where each term is r times larger than the previous term. Sum the first 20 terms of the sequence: 1, 3, 5, 7, 9. You may need to be able to prove this formula. The sum to n terms of an arithmetic progression U n = 3 + 2(n - 1) = 2n + 1, which we already knew. In general, the nth term of an arithmetic progression, with first term a and common difference d, is: a + (n - 1)d. The terms in the sequence are said to increase by a common difference, d.įor example: 3, 5, 7, 9, 11, is an arithmetic progression where d = 2. In the above example, U r = 3r + 2 and n = 3.Īn arithmetic progression is a sequence where each term is a certain number larger than the previous term. up to and including n in turn for r in U r. For the sequence U r, this means the sum of the terms obtained by substituting in 1, 2, 3. Now add up all of the term that you have written down. ![]() Keep doing this until you get to 4, since this is the number above the S. ![]() Then replace r by 2 and write down what you get. ![]() This means replace the r in the expression by 1 and write down what you get. The Greek capital sigma, written S, is usually used to represent the sum of a sequence. , the sum to 3 terms = S 3 = 2 + 4 + 6 = 12. The series of a sequence is the sum of the sequence to a certain number of terms.
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