3 Consider the geometric series: \( 45+15+5+\ldots \) 3.1 Does the sequence converge or diverge? Justify your answer. 3.2 Determine the sum to infinity of the series, if it exists.

The sequence converges because the absolute value of the common ratio \( r \) is less than 1. In this series, the first term \( a = 45 \) and the common ratio can be found by dividing the second term by the first, \( r = \frac{15}{45} = \frac{1}{3} \). Since \( |r| < 1 \), the geometric series converges. The sum to infinity of a converging geometric series can be calculated using the formula \( S = \frac{a}{1 - r} \). Here, \( S = \frac{45}{1 - \frac{1}{3}} = \frac{45}{\frac{2}{3}} = 45 \times \frac{3}{2} = 67.5 \). Thus, the sum to infinity is 67.5.