![]() ![]() Where a is the first term in the sequence, r is the common ratio between the terms, and n is the number of terms in the sequence. To find the sum of a finite geometric sequence, use the following formula: For example, 1 + 3 + 9 + 27 + 81 = 121 is the sum of the first 5 terms of the geometric sequence. r -1 What is the ninth term of the sequence 5, 15, 45, Find the common ratio. r > 1: sequence approaches positive infinity if a > 0 or negative infinity if a If r is negative, the sign of the terms in the sequence will alternate between positive and negative. ![]() ![]() If r is not -1, 1, or 0, the sequence will exhibit exponential growth or decay. The calculator will generate all the work with detailed explanation. Also, it can identify if the sequence is arithmetic or geometric. The sequence is indeed a geometric progression where a1 3 and r 2. :: Sequences Calculators :: Find n th term N th term of an arithmetic or geometric sequence The main purpose of this calculator is to find expression for the n th term of a given sequence. You use n in the general formula of a geometric sequence and replace it with a number when you want to find the term in a certain position. Solution Begin by finding the common ratio, r 6 3 2 Note that the ratio between any two successive terms is 2. Ī n = ar n-1 = 1(3 (12 - 1)) = 3 11 = 177,147ĭepending on the value of r, the behavior of a geometric sequence varies. Saying 'the nth term' means you can calculate the value in position n, allowing you to find any number in the sequence. Find the 12 th term of the geometric series: 1, 3, 9, 27, 81. ![]()
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