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Expert: Sherry Wallin - 11/30/2010


Question

Sequences and Series
Miss Sherry,
            Thank god you arent maxed out right now! I typed in one Question to Mervyn but I aint getting any answers at all from him since 5 days,and from the last 2 days ,I see you maxed out whenever I open!So,now I finally got a chance to ask you! Thus,
         I have uploaded a question below. I know the answer and I am writing it over here.Can you please tell me what I can add more to make it really seem thorough.It is from sequences section hence I am supposed to write the general term of geometric sequence too, but I dont know how should I figure it out.Plus,can you please tell whether it is correct or not.Hence,following is the answer:
Let x, be the original price the farmer was paid, then
 x * 1.2 * 1.2 * 1.2  =  $0.80                          
 1.728 x = .80
 x = .80/1.728= .46
                         Thankyou very much!
                           Xiang.


Answer
Hi Xiang~

If I am interpreting this correctly then you have the original price call it a. Then at the end of the first stage the price is a + .2a =
a(1 + .2) = 1.2a and at the end of the 2nd stage the price is 1.2a(1.2)= (1.2)^2a and at the end of the 3rd stage is 1.2((1.2)^2)a = ((1.2)^3)a. The sum of these needs to be equal to .8.
i.e., a + 1.2a + 1.2^2a + 1.2^3a needs to equal .8

according to the geometric series this is a(1-r^n)/(1-r). Here n is 4 because there are 4 terms, the constant or original cost plus the 3 increases, thus a(1-1.2^4)/(1-1.2) = a(-1.0736/-.2)= 5.368a which has to equal 80 cents thus a = 8/5.368 => a = .149.

You can check this in the sum of
.149 + .149(1.2) + .149(1.2)^2 + .149(1.2)^3 = .799832 which means that the original cost was about 15 cents.

Math Prof

    Questioner's Rating
    Rating(1-10)Knowledgeability = 10Clarity of Response = 10Politeness = 10
    CommentMiss Sherry, Awesome! Your speed of answering the qusetion is as good as light! :) :) :) Thankyou so Much!,Xiang.


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Sherry Wallin

Expertise

I can answer most questions up through Calculus and some in Number Theory and Abstract Algebra.

Experience

I have had my Bachelor's Degree since 1987 and have been a teacher since 1988. I earned my Masters Degree in Mathematics May 2010. I have been teaching at the same community college since 2002.

Education/Credentials
I have taught 12 years at the community college level, medical college, and technical college as well as a high school instructor and alternative education instructor and charter school instructor.

Awards and Honors
Master's GPA 3.56 Bachelor's GPA 3.34 Post grad work not degree related GPA 4.0

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