Question

1. graph y = 7^x. 8. graph y = (1/3)^x. 9. write an equation for the nth term of the geometric sequence -3, 9, -27, ...

Explanation:

Step1: Identify the first - term and common ratio

For the geometric sequence \(a_1=-3\), and the common ratio \(r=\frac{9}{-3}=- 3\).

Step2: Use the formula for the nth term of a geometric sequence

The formula for the nth term of a geometric sequence is \(a_n=a_1r^{n - 1}\). Substitute \(a_1=-3\) and \(r = - 3\) into the formula: \(a_n=-3\times(-3)^{n - 1}\).

Step3: Simplify the expression

Using the rule of exponents \(a^m\times a^n=a^{m + n}\), we can rewrite \(a_n=-3\times(-3)^{n - 1}=(-3)^{1+(n - 1)}=(-3)^n\).

Answer:

\(a_n=(-3)^n\)