How to Find Fraction Sequences

How to Find Fraction Sequences
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Algebra class will frequently require you to work with sequences, which can be arithmetic or geometric. Arithmetic sequences will involve obtaining a term by adding a given number to each previous term, while geometric sequences will involve obtaining a term by multiplying the previous term by a fixed number. Whether or not your sequence involves fractions, finding such a sequence hinges on determining whether the sequence is arithmetic or geometric.

    Look at the terms of the sequence and determine whether it is arithmetic or geometric. For example, 1/3, 2/3, 1, 4/3 is arithmetic, since you obtain every term by adding 1/3 to the previous term. But 1, 1/5, 1/25, 1/125, on the other hand, is geometric, since you obtain each term by multiplying the previous term by 1/5.

    Write an expression that describes the nth term of the series. In the first example, A(n) = A(n) - 1 + 1/3. Therefore, when you plug in n = 1 to find the first term of the series, you will find that it equals A0 + 1/3, or 1/3. When you plug in n = 2, you find that it equals A1 + 1/3, or 2/3. In the second example, A(n) = (1/5)^(n - 1). Therefore, A1 = (1/5)^0, or 1, and A2 = (1/5)^1, or 1/5.

    Use the expression that you wrote in Step 2 to determine any arbitrary term in the series, or to write the first several terms. For instance, you can use the expression A(n) = (1/5)^(n - 1) to write the first 10 terms of the series, 1,1/5,1/25, 1/125, (1/5)^4,(1/5)^5,(1/5)^6,(1/5)^7,(1/5)^8 and (1/5)^9, or to find the hundredth term, which is (1/5)^99.

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