select the correct answer. paul started a construction company. in the first year, his company built 6…

select the correct answer. paul started a construction company. in the first year, his company built 6 structures. the number of structures that his company built doubled every year. how many structures did pauls company build in the 5th year? a. 96 structures b. 192 structures c. 186 structures d. 90 structures

select the correct answer. paul started a construction company. in the first year, his company built 6 structures. the number of structures that his company built doubled every year. how many structures did pauls company build in the 5th year? a. 96 structures b. 192 structures c. 186 structures d. 90 structures

Answer

Explanation:

Step1: Identify the initial - value and the rule

The company built 6 structures in the first year and the number of structures doubles every year.

Step2: Use the formula for a geometric - sequence

The formula for a geometric sequence is $a_n=a_1r^{n - 1}$, where $a_1$ is the first - term, $r$ is the common ratio, and $n$ is the number of terms. Here, $a_1 = 6$, $r = 2$, and $n=5$.

Step3: Calculate the number of structures in the 5th year

Substitute the values into the formula: $a_5=6\times2^{5 - 1}=6\times2^4=6\times16 = 96$.

Answer:

A. 96 structures