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.


About the Author

Tricia Lobo has been writing since 2006. Her biomedical engineering research, "Biocompatible and pH sensitive PLGA encapsulated MnO nanocrystals for molecular and cellular MRI," was accepted in 2010 for publication in the journal "Nanoletters." Lobo earned her Bachelor of Science in biomedical engineering, with distinction, from Yale in 2010.