The first term of a G.P. is 1 and the sum to infinity is 5. Find the common ratio.
Question
The first term of a G.P. is 1 and the sum to infinity is 5. Find the common ratio.
Solution
The sum to infinity of a geometric progression (G.P.) is given by the formula S = a / (1 - r), where 'a' is the first term and 'r' is the common ratio.
Given that the first term 'a' is 1 and the sum to infinity 'S' is 5, we can substitute these values into the formula:
5 = 1 / (1 - r)
To solve for 'r', we first multiply both sides of the equation by (1 - r):
5 * (1 - r) = 1
Expanding the left side gives:
5 - 5r = 1
Subtracting 5 from both sides gives:
-5r = 1 - 5
Solving for 'r' gives:
r = (1 - 5) / -5
So, the common ratio 'r' is 4/5 or 0.8.
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