70) Which of the following best describes the series \( \sum_{k=1}^{100} 3(5)^{k-1} \) ?

This series is a geometric series where the first term \( a = 3 \) and the common ratio \( r = 5 \). The series can be expressed as \( 3 + 3 \cdot 5 + 3 \cdot 5^2 + \ldots + 3 \cdot 5^{99} \). The sum of a finite geometric series can be computed using the formula \( S_n = \frac{a(1 - r^n)}{1 - r} \), where \( n \) is the number of terms. Here, plugging in the values will allow you to find the sum. To calculate it, you would set \( n = 100 \), so you would compute \( S_{100} = \frac{3(1 - 5^{100})}{1 - 5} = \frac{3(1 - 5^{100})}{-4} = -\frac{3(1 - 5^{100})}{4} \). This gives you a concrete result for the sum, showcasing how powerful and efficient geometric series can be in mathematics!