Does anyone know how to answer this exercise?
1 answer:
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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
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
So, the formula for the sequence in question is
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
Substituting
Hence, the correct option is option number 1