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What is a geometric progression?

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A geometric progression is one in which each term is derived by multiplying the preceding term by a given number r, called the common ratio; it has the general form a, ar, ar2,?…?, arn-1,?…?, where a and n have the same meanings as above; e.g., the progression 1, 2, 4, 8,?… is geometric with a =1 and r =2. The value of the 10th term, i.e., when n =10, is given as 1·2 10-1 =2 9 =512. The sum of the geometric progression is given by the formula a (1- rn)/(1- r) for the first n terms.

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