SOLUTION: The number of trees damaged reported over a four year period 20, 41,83,167 Find the recursive formula and predict how many trees will be damaged in the seventh year if this tren

Algebra ->  Sequences-and-series -> SOLUTION: The number of trees damaged reported over a four year period 20, 41,83,167 Find the recursive formula and predict how many trees will be damaged in the seventh year if this tren      Log On


   

Question 1193484: The number of trees damaged reported over a four year period 20, 41,83,167 Find the recursive formula
and predict how many trees will be damaged in the seventh year if this trend continues?
Answer by ikleyn(52788) About Me  (Show Source):
You can put this solution on YOUR website!
.

The recursive formula is (or can be taken in the form)

    N(k) = 2*N(k-1) + 1,  k = 2, 3, 4


for given values.



Please check it on your own that this formula really works.



When you complete checking and will prove for yourself that the formula works,

you may use it to move further and predict/calculate  N(k)  for k = 5, 6 and 7.



I leave this simple job for you.



You may report me about your progress.


Happy learning (!)


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Comment from student :   i did get  t7=1321  is that correct? thank you


My response :   To answer your question,  I prepared this Table below 

    T      A      B      L      E


  k            Given         Calculated 
               numbers       using the formula

 ------------------------------------

  1		20		20
  2		41		41
  3		83		83
  4		167		167
  5				335
  6				671
  7				1343


First column is for index "k";

second column is the given numbers;

third column are the numbers calculated using the recursive formula.



From the Table, you see, that the formula correctly reproduces the given numbers.



Next, you see that the 7-th term is 1343, which does not coincide with your value.



So, your answer is INCORRECT.



Look for the error/errors in your computations.