Find the recursive and closed formula for the sequences below. Then we have, Recursive definition: an ran 1 with a0 a. Suppose the initial term a0 is a and the common ratio is r. The difference between an arithmetic and a geometric sequenceĪrithmetic sequences are formed by adding or subtracting the same number. A geometric sequence, or geometric progression, is a sequence of numbers where each successive number is the product of the previous number and some constant r. A sequence is called geometric if the ratio between successive terms is constant.When we add the terms of geometric sequence. This is not always the case as when r is raised to an even power, the solution is always positive. The geometric sequence formula for nth term is a r(n-1), where a is the first term, r is the common ratio. A negative value for r means that all terms in the sequence are negative.Each term is the product of the common ratio and the previous. 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. A recursive formula allows us to find any term of a geometric sequence by using the previous term.
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