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Robin bought a computer for $1,250. It will depreciate, or decrease in value, by 10% each year that she owns it. a) Is the sequence formed by the value at the beginning of each year arithmetic, geometric, or neither? Explain. b) Write an explicit formula to represent the sequence. c) Find the value of the computer at the beginning of the 6th year.

Caroline Campbell

in Mathematics

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Alexa Spicer on July 20, 2018

Remember that the general formula of a geometric sequence is where is the n th term is the difference is in the place of the word in the sequenceAlso, to find we use the formula: where is the current term of the sequence is the previous term (a) Allows to find the first three terms of our sequence to check what type of sequence:we know that for our problem the initial value of the computer is $1250, so our first term is from 1250. In other words .To fin our second term , we will subtract 10% of the value to our original value , and therefore to find our third term, we will subtract even more the 10% of our present value: and , soNow that we have our sequence allows you to check if we have a consistent way to demonstrate that we have a geometric progression:- and : - with , and : Look! our s are the same, so we can conclude that we have a geometric progression.b) To do this we just have to replece the values of our sequence in the general formula of a geometric sequence. We know that from our previous point and that . So let's substitute the values in the geometric progression formula to find the explicit formula:c) To find the value of the equipment at the beginning of the 6th year, we just have to find the 6th therm in our geometric progression:we can conclude that the value of the equipment at the beginning of the 6th year will be $738.1125


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