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.

Question

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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