Answer:
1/2
Explanation:
You want the common ratio of a geometric series whose sum is 10 and whose second term is 5/2.
Second term
For first term a1 and common ratio r, the second term is ...
a2 = a1·r
Sum
The sum to infinity of the series is ...
S = a1/(1 -r)
Solution
Dividing the first equation by the second, we have ...
(5/2)/10 = (a1·r)/(a1/(1-r))
5/20 = r(1 -r)
r² -r +1/4 = 0 . . . . . . put in standard form
(r -1/2)² = 0
The solution is the value of r that makes the factors be zero: r = 1/2.
The constant ratio is 1/2.
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Additional comment
The first term is 5.