In your early days of studying Algebra, lessons deal with both algebraic and geometric sequences. Identifying patterns is also a must in Algebra. When working with fractions, these patterns can be algebraic, geometric or something completely different. The key to noticing these patterns is to be vigilant and hyper-aware of potential patterns among your numbers.
Determine whether a given quantity is added to each fraction, to obtain the next fraction. For instance, if you have the sequence 1/8, 1/4, 3/8, 1/2 -- if you make all the denominators equal to 8, you will notice that the fractions increase from 1/8 to 2/8 to 3/8 to 4/8. Therefore, you have an arithmetic sequence, in which the pattern involves adding 1/8 to each fraction to obtain the next.
Determine whether a "factor" pattern, known as a geometric sequence, exists among the fractions. In other words, determine if a number is multiplied by each fraction to obtain the next. If you have the sequence 1/(2^4), 1/(2^3), 1/(2^2), 1/2, which can also be written as 1/16, 1/8, 1/4, 1/2, notice that you must multiply each fraction by 2 to obtain the next one.
Determine -- if you see neither an algebraic or geometric sequence -- whether the problem is combining an algebraic and/or geometric sequence with another mathematical operation, such as working with the reciprocals of fractions. For instance, the problem could give you a sequence such as 2/3, 6/4, 8/12, 24/16. You' ll notice that the second and fourth fractions in the sequence are equal to the reciprocals of 2/3 and 8/12, in which both the numerator and denominator is multiplied by 2.
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.
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