Transcription of Geometric Sequences
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Geometric Sequences
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.
Example 2 (Continued): Step 2: Now, to find the fifth term, substitute n =5 into the equation for the nth term. 51 5 4 1 6 3 1 6 3 6 81 2 27 a ⎛⎞− Step 3: Finally, find the 100th term in the same way as the fifth term. 100 1 5 99 99 98 1 6 3 1 6 3 23 3 2 3 a ⎛⎞− ⋅ = = Example 3: Find the common ratio, the fifth term and the nth term of the geometric sequence. (a) −−
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