what are the values of $a_1$ and $r$ of the geometric series?\n1 + 3 + 9 + 27 + 81\n$a_1 = 1$ and…

what are the values of $a_1$ and $r$ of the geometric series?\n1 + 3 + 9 + 27 + 81\n$a_1 = 1$ and $r=\frac{1}{3}$\n$a_1=\frac{1}{3}$ and $r = 1$\n$a_1 = 1$ and $r = 3$\n$a_1 = 3$ and $r = 1$

what are the values of $a_1$ and $r$ of the geometric series?\n1 + 3 + 9 + 27 + 81\n$a_1 = 1$ and $r=\frac{1}{3}$\n$a_1=\frac{1}{3}$ and $r = 1$\n$a_1 = 1$ and $r = 3$\n$a_1 = 3$ and $r = 1$

Answer

Explanation:

Step1: Identify the first - term

In a geometric series (a_1 + a_2+a_3+\cdots), the first - term (a_1) is the first number in the series. For the series (1 + 3+9 + 27+81), (a_1 = 1).

Step2: Calculate the common ratio (r)

The common ratio (r) of a geometric series is given by (r=\frac{a_{n + 1}}{a_n}). Let's take (n = 1), then (r=\frac{a_2}{a_1}). Since (a_1 = 1) and (a_2 = 3), (r=\frac{3}{1}=3).

Answer:

C. (a_1 = 1) and (r = 3)