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how do you find the general term of a geometric sequence. Create a table with headings n and a n where n denotes the set of consecutive positive integers and a n represents the term corresponding to the positive integers. If your pre-calculus teacher gives you any two nonconsecutive terms of a geometric sequence you can find the general formula of the sequence as well as any specified term.
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The general geometric sequence can be expressed as. If you find a common ratio between pairs of terms then you have a geometric sequence and you should be able to determine a_0 and r so that you can use the general formula for terms of a geometric sequence. We actually have a formula that we can use to help us calculate the general term or nth term of any geometric sequence.
T 1 a ar0 T 2 a r ar1 T 3 a r r ar2 T 4 a r r r ar3 T n a r rn 1 times arn1 T 1 a a r 0 T 2 a r a r 1 T 3 a r r a r 2 T 4 a r r r a r 3 T n a r r n 1 times a r n 1.
Other problems will ask you general questions about the characteristics of a geometric. As you can see each term is found by multiplying 2 a common ratio to the previous term. In mathematics geometric series and geometric sequences are typically denoted just by their general term aₙ so the geometric series formula would look like this. The terms of a geometric sequence can be found by beginning with the first term and multiplying by the common ratio repeatedly.
