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.
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