write an equation to describe the sequence below. use n to represent the position of a term in the sequence…

write an equation to describe the sequence below. use n to represent the position of a term in the sequence, where n = 1 for the first term. 11, -33, 99, ... write your answer using decimals and integers. a_n = ( )^{n - 1}

write an equation to describe the sequence below. use n to represent the position of a term in the sequence, where n = 1 for the first term. 11, -33, 99, ... write your answer using decimals and integers. a_n = ( )^{n - 1}

Answer

Explanation:

Step1: Identify the first - term

The first - term $a_1$ of the sequence is 11. When $n = 1$, we want $a_1$ to be 11. In the general formula for a geometric sequence $a_n=a_1r^{n - 1}$, the first - term $a_1$ is the number that goes in the first blank. So $a_1 = 11$.

Step2: Find the common ratio $r$

To find the common ratio $r$, divide the second term by the first term. $r=\frac{a_2}{a_1}=\frac{-33}{11}=- 3$. We can double - check by dividing the third term by the second term: $\frac{a_3}{a_2}=\frac{99}{-33}=-3$.

Answer:

$a_n = 11(-3)^{n - 1}$