This means that because of the annuity, the couple earned $720.44 interest in their college fund.
Sum of geometric sequence proof series#
Notice, the couple made 72 payments of $50 each for a total of 72\left(50\right) = $3,600. A geometric series sum(k)ak is a series for which the ratio of each two consecutive terms a(k+1)/ak is a constant function of the summation index k. We can write the sum of the first n terms of a geometric series asģ20.44Īfter the last deposit, the couple will have a total of $4,320.44 in the account. Recall that a geometric sequence is a sequence in which the ratio of any two consecutive terms is the common ratio, r. A geometric sequence18, or geometric progression19, is a sequence of numbers where each successive number is the. Students should also have completed the following Teaching and Learning Plans: Arithmetic Sequences, Arithmetic Series and Geometric Sequences.
Just as the sum of the terms of an arithmetic sequence is called an arithmetic series, the sum of the terms in a geometric sequence is called a geometric series. The nth partial sum of a geometric sequence can be calculated using the first term a1 and common ratio r as follows: Sna1(1rn)1r.
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