Answer:
Converges
Sum = 20.8333
Step-by-step explanation:
A geometric series has a general formula of:
[tex]\sum ar^n[/tex]
Where 'a' is the initial term, 'n' is the number of terms, and 'r' is the constant ratio. If |r| < 1 than the series converges.
In this particular case, the initial term is a=25, and each term is being divided by -5, or multiplied by -0.2, so the general form would be:
[tex]\sum 25*(-0.2)^n[/tex]
Since 0.2 < 1.0, the series converges.
The sum of the series is given by:
[tex]S=\frac{a}{1-r}\\S=\frac{25}{1-(-0.2)}\\S=20.8333[/tex]
The sum is 20.8333.
The geometric series converges and the sum is equal to 20.83.
A geometric series is the sum of an infinite number of terms that have a constant ratio between successive terms .
A geometric series has a general formula of:
∑arⁿ
Where 'a' is the initial term, 'n' is the number of terms, and 'r' is the constant ratio. If |r| < 1 than the series converges.
In this particular case, the initial term is a=25 and each term is divided by -5 or multiplied by (-0.2)
Therefore r = -0.2 and as it is <1 therefore the series converges
The sum of a convergent series is
S = a/(1-r)
S = 25/(1-(-0.2))
S= 25/1.2
S = 20.83
Therefore the sum of the series is 20.83
To know more about Geometric Series
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