Transcription of Geometric Sequences - Alamo Colleges District
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Geometric Sequences - Alamo Colleges District
Geometric Sequences Another simple way of generating a sequence is to start with a number a and repeatedly multiply it by a fixed nonzero constant r . This type of sequence is called a Geometric sequence. Definition: A Geometric sequence is a sequence of the form 234,,,,, ..aarar ar ar The number a is the first term, and r is the common ratio of the sequence. The nth term of a Geometric sequence is given by 1nnaar =. The number r is called the common ratio because any two consecutive terms of the sequence differ by a multiple of r, and it is found by dividing any term 1na+ after the first by the preceding term . That is na 1nnara+=. Is the Sequence Geometric ? Example 1: Determine whether the sequence is Geometric . If it is Geometric , find the common ratio. (a) 2, 8, 32, 128, ..(b) 1 , 2, 3, 5, 8, .. Solution (a): In order for a sequence to be Geometric , the ratio of any term to the one that precedes it should be the same for all terms.
Example 2: Find the nth term, the fifth term, and the 100th term, of the geometric sequence determined by . 1 6, 3 ar==. Solution: To find a specific term of a geometric sequence, we use the formula . for finding the nth term. Step 1: The nth term of a geometric sequence is given by . n 1 aar. n = − So, to find the nth term, substitute the ...
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