Find the common ratio r to make 5, x, y, 32 as a part of a geometric sequence.

The common ratio r for the geometric sequence 5, x, y, and 32 is determined by the equation 5 r 3 = 32 . Solving this gives r = 3 5 ​ 2 ​ . Thus, this ratio allows the sequence to be geometric as each term can be expressed in terms of this ratio multiplied by its predecessor.
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Answered by Anonymous | 2025-07-04

To find the common ratio r in a geometric sequence, we need to ensure that each term is the product of the previous term and the common ratio.
For the sequence 5 , x , y , 32 , we want each term to fit the geometric progression model:

The second term x can be expressed as 5 r because it follows the first term.

The third term y can be expressed as 5 r 2 because it follows the second term.

The fourth term is given as 32, which can be expressed as 5 r 3 .


Next, we solve the equation for the common ratio r :
5 r 3 = 32
To find r , divide both sides by 5:
r 3 = 5 32 ​
Now, take the cube root on both sides to solve for r :
r = 3 5 32 ​ ​
Calculating this, we get:
r ≈ 1.682
Therefore, the common ratio r for this geometric sequence is approximately 1.682. This means each term is about 1.682 times the previous term.

Answered by RyanHarmon181 | 2025-07-06