Let us say we were given this geometric sequence. The recursive rule means to find any number in the sequence, we must multiply the common ratio to the previous number in this list of numbers. To determine any number within a geometric sequence, there are two formulas that can be utilized. where n is any positive integer greater than 1. The r-value, or common ratio, can be calculated by dividing any two consecutive terms in a geometric sequence. This notation is necessary for calculating nth terms, or a n, of sequences. This means that if we refer to the tenth term of a certain sequence, we will label it a 10. Mathematicians also refer to generic sequences using the letter a along with subscripts that correspond to the term numbers as follows: Mathematicians use the letter r when referring to these types of sequences. So that we can examine these sequences to greater depth, we must know that the fixed numbers that bind each sequence together are called common ratios. The fourth number times -1/2 is the fifth number: -2 × -1/2 = 1.īecause these sequences behave according to this simple rule of multiplying a constant number to one term to get to another, they are called geometric sequences. This too works for any pair of consecutive numbers. We need to multiply by -1/2 to the first number to get the second number. Sequence C is a little different because it seems that we are dividing yet to stay consistent with the theme of geometric sequences, we must think in terms of multiplication. The third number times 6 is the fourth number: 0.36 × 6 = 2.16, which will work throughout the entire sequence. This also works for any pair of consecutive numbers. The second number times 2 is the third number: 2 × 2 = 4, and so on.įor sequence B, if we multiply by 6 to the first number we will get the second number. This works for any pair of consecutive numbers. įor sequence A, if we multiply by 2 to the first number we will get the second number. The following sequences are geometric sequences: Sequences of numbers that follow a pattern of multiplying a fixed number from one term to the next are called geometric sequences.
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