The sum of the given geometric progression to the nearest hundredth is 7.50
Sum of a geometric progression
The given nth term is an explicit formula for a geometric sequence. The formula for calculating the sum of the given expression is;
Sum = a(1-r^n)/1-r
where
r is the common ratio. = 1/2
n is the number of terms = 10
a is the first term = 5
Substitute to have:
Sum = 5(1-(1/3)^10)/1-1/3
Sum = 5(1-1/59049)/2/3
Sum = (5 - 5/59049) * 3/2
sum = 7.50
Hence the sum of the given geometric progression to the nearest hundredth is 7.50
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