SOLUTION: write a recursive formula for each of the following sequences. and find the 10th term. Use u1 for the first term given. a. 100, 150, 225, 337.5, 506.25... b. 73.4375, 29.375, 1

Algebra ->  Algebra  -> Coordinate Systems and Linear Equations -> SOLUTION: write a recursive formula for each of the following sequences. and find the 10th term. Use u1 for the first term given. a. 100, 150, 225, 337.5, 506.25... b. 73.4375, 29.375, 1      Log On

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Question 160185: write a recursive formula for each of the following sequences. and find the 10th term. Use u1 for the first term given.
a. 100, 150, 225, 337.5, 506.25...
b. 73.4375, 29.375, 11.75, 4.7, 1.88...
c. 80.00, 82.40, 84.87, 87.42, 90.04....
d. 208.00, 191.36, 176.05, 161.97
Answer by Edwin McCravy(8999) About Me  (Show Source):
You can put this solution on YOUR website!

a. 100, 150, 225, 337.5, 506.25...

Question: What do we have to multiply u%5B1%5D=100 by to get u%5B2%5D=150?
Answer: To find out we divide 150 by 100 and get 1.5.

Question: What do we have to multiply u%5B2%5D=150 by to get u%5B3%5D=225?
Answer: To find out we divide 225 by 150 and get 1.5

Question: What do we have to multiply u%5B3%5D=225 by to get u%5B4%5D=337.5?
Answer: To find out we divide 337.5 by 225 and get 1.5

Question: What do we have to multiply u%5B4%5D=337.5 by to get u%5B5%5D=506.25?
Answer: To find out we divide 150 by 100 and get 1.5

So we generalize:

So in each case above, what did we have to multiply u%5Bn%5D by to get 
+matrix%281%2C1%2C+%27u%5Bn%2B1%5D%27%29++?
Answer: We had to multiply it by 1.5.

What did we start with?  
Answer: We started with a%5B1%5D=100.

So how do we write the recursive formula:

Answer:



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b. 73.4375, 29.375, 11.75, 4.7, 1.88...

Do it exactly the same way:

Answer


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c. 80.00, 82.40, 84.87, 87.42, 90.04....

Do it exactly the same way, except we must always round to
the nearest hundredth:

Answer


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d. 208.00, 191.36, 176.05, 161.97

Same as c:

Answer


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Edwin