SOLUTION: What is the sixth term when the first term is 4 and the common ratio is 3?

Question 71049: What is the sixth term when the first term is 4 and the common ratio is 3?
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
This is a geometric progression because each term after the first term is obtained by multiplying the preceding term by a fixed number called the common ratio. In this case you can almost solve it faster by actually doing the multiplication than by using the equation that applies.
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Say to yourself:
Start with 4 and multiply it by 3 to get the SECOND term of 12.
Then say multiply 12 times 3 to get the THIRD term of 36.
Then say multiply 36 times 3 to get the FOURTH term of 108.
Then say multiply 108 times 3 to get the FIFTH term of 324.
And finally say multiply 324 times 3 to get the SIXTH or last term of 972.
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The answer is that the sixth term is 972.
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The equation that you can use is:
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where the definitions of the letters are:
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L is the value of the Last Term. (In this case as we saw above L turns out to be 972.)
A is the first term. (In this problem A = 4.)
R is the common ratio. (For this problem, that ratio is given as 3.)
N is the number of the term you are looking for. (In this case it is 6.)
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So, to use the equation all we need to do is plug 4 in for A, 3 in for R, and 6 in for N. The equation is then:
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and using a calculator or multiplying by hand you can determine that . With that you reduce the equation to:
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and when you multiply that out you find that L (the value of the Last or sixth term) is 972, the same answer as we got by just using the definition of geometric progression and applying our numbers to calculate each term. Obviously if the number of the term is big (for example, find the 99th term) the first way would be a lot of work, and the equation method would be much easier.
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Hope this helps to clarify things for you a little.
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