Question

1-find the common ratio and the seventh term of the following sequence :2÷9,2÷3,6,18.
2- the first term of a geometric series is 1 and the fourth term is 27.find the sum of the first terms.

Answer 1

1) The common ratio is

$$q=\frac{18}{6}=3$$

$$b_7=b_1q^{7-1}=\frac{2}{9}3^{6}=162$$

2)

$$b_4=1q^{4-1}=q^3=27$$

$$q=3$$

The sum of the first n terms:

$$S_n=1\frac{1-3^n}{1-3}=\frac{3^n-1}{2}$$