Question

(100 points) What is the common ratio of the geometric sequence? (graph attached)

Answer 1

`(3)/(4)`

Explanation:

In a geometric sequence, each term is obtained by multiplying the preceding term by a constant factor, which is known as the common ratio (r). Therefore, to find the common ratio, we can simply divide any term by its preceding term:

`r = (a(n+1))/(a(n))`

From the given graph, the first and second terms are:

• a(1) = 16
• a(2) = 12

Substituting these into the formula gives:

`r = (a(2))/(a(1))=(12)/(16)=(3 * 4)/(4 * 4)=(3)/(4)`

So, the common ratio of the given geometric sequence is 3/4.