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Consider the sequence 1, –3, 9, –27, 81, … Which statement describes the sequence?
The sequence diverges.
The sequence converges to 0.
The sequence converges to 1.
The sequence converges to ∞.
There is a similar problem with the same numbers except with no negatives so it goes 1 , 3 , 9 , 27, 81 for this question the answer is that it diverges.
Step-by-step explanation:
It was on the unit test review for edge and the answer was that it diverges.
This is about understanding the behavior limits of sequence.
The sequence diverges.
The given sequence is;
1, –3, 9, –27, 81,...
Now, from the sequence above, we can see that each number is multiplied by -3 to get the next one in the sequence.
From mathematical definition, A divergent sequence is one in which the values are approaching an infinite value which could either be positive or negative whereas if it is a convergent sequence it will be approaching 0.
In this sequence given, we can see that the values are increasing to either positive or negative and as such it will keep changing till an infinite positive or negative value which corresponds with the definition of a divergent sequence as earlier defined.
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