Find the sum to infinity of the geometric progression whose first term is 6 and whose second term is 4.
Solution
The first term of the geometric progression is given as \(a = 6\).
The second term is given as \(ar = 4\), where \(r\) is the common ratio.
We can find \(r\) by solving the equation \(6r = 4\).
Thus, \(r = \frac{4}{6} = \frac{2}{3}\).
The formula for the sum to infinity of a geometric progression is \(S_\infty = \frac{a}{1-r}\), provided \(|r| < 1\).
Substituting the values, we get \(S_\infty = \frac{6}{1 - \frac{2}{3}}\).
Calculating further, \(S_\infty = \frac{6}{\frac{1}{3}} = 6 \times 3 = 18\).
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