![]() What are the series types There are various types of series to include arithmetic series. It is represented by the formula an a1 r (n-1), where a1 is the first term of the sequence, an is the nth term of the sequence, and r is the common ratio. Geometric sequences are formed by multiplying or dividing the same number. A series represents the sum of an infinite sequence of terms. A geometric sequence is a sequence of numbers in which each term is obtained by multiplying the previous term by a fixed number. To recall, an geometric sequence or geometric progression is a sequence of numbers where each term after the first is found by multiplying the previous one by a. The difference between an arithmetic and a geometric sequenceĪrithmetic sequences are formed by adding or subtracting the same number.The nth term of a GP is Tn ar Common ratio r Tn/ T The formula to calculate the sum of. This is not always the case as when r is raised to an even power, the solution is always positive. The general form of terms of a GP is a, ar, ar2, ar3, and so on. ![]() ![]() A negative value for r means that all terms in the sequence are negative.Mixing up the common ratio with the common difference for arithmetic sequencesĪlthough these two phrases are similar, each successive term in a geometric sequence of numbers is calculated by multiplying the previous term by a common ratio and not by adding a common difference. Saying 'the nth term' means you can calculate the value in position n, allowing you to find any number in the sequence. ![]()
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