The trees at a national park have been increasing in numbers. there were 1,000 trees in the first year that the park started tracking them. since then, there has been one fifth as many new trees each year. create the sigma notation showing the infinite growth of the trees and find the sum, if possible.

1 1000
2 200
3 40

The sequence forms a Geometric sequence as the rule to obtain the value for the next term is by ratio

Term 1: 1000
Term 2: 200
Term 3: 40

From term 1 to term 2, there's a decrease by 
From term 2 to term 3, there's a decrease also by 

The rule to find the  term in a sequence is 
, where  is the first term in the sequence and  is the ratio

So, the formula for the sequence in question is
term = 

The sequence is a divergent one. We can always find the value of the next term by dividing the previous term by 5 and if we do that, the value of the next term will get closer to 'zero' but never actually equal to zero.

We can find a partial sum of the sequence using the formula
for -1<r<1 
Substituting  and  we have 
=  = 1250

Hence, the correct option is option number 1