Question
Tue February 26, 2013 By:

Each year a tree grows by 5cm less than the preceding year. If it grew by 1m in the first year of survey, in how many years will it have caesed growing?

Expert Reply
Tue February 26, 2013
In the first year the tree grew by 1m
In the second year, it will grow by  (1- 0.05)m = 0.95m
In the thirs year, it will grow by (0.95 - 0.05)m = 0.9 m and so on...
 
So, this is actually an AP, where the first term (a) = 1 and d = -0.05m
We want to find the n, such that an = 0
 
an = a+(n-1)d
0 = 1+(n-1) (-0.05)
0.05n = 1.05
n = 21 years
 
So, afer 21 years, the tree would have stopped growing. 
 
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