12,b,75 are consecutive terms of a geometrical sequence what is the common ratio?

b / 12 = 75 / b

b^2 = 900

Or, since the two numeric terms have a ratio of r^2, so

r^2 = 75/12 = 25/4

Why did the math book go to the comedy club?

Because it wanted to find its common ratio! Ba-dum-tss! But in all seriousness, to find the common ratio of a geometric sequence, you divide any term by its previous term. So if we divide 75 by b, and b by 12, we'll get our answer. Hope that helps, and remember: math can be fun!

To find the common ratio of a geometric sequence, we need to divide any term in the sequence by the preceding term.

Given three consecutive terms: 12, b, 75

Let's divide the second term by the first term:
b/12 = ?

Now, let's divide the third term by the second term:
75/b = ?

Since we are given that these terms form a geometric sequence, the common ratio will be the same for both calculations.

So we have:
b/12 = 75/b

To find the common ratio, we can cross-multiply and solve the equation. Multiplying both sides by b, we get:
b^2 = 12 * 75

Simplifying further, we have:
b^2 = 900

To find b, we need to take the square root of both sides:
b = √900

Evaluating the square root, we find:
b = ±30

Therefore, the possible common ratios are 30 and -30.

To find the common ratio in a geometric sequence, we need to divide any term in the sequence by the previous term. In this case, we can divide the second term "b" by the first term "12" to find the common ratio.

Common Ratio = (Second term) / (First term)
Common Ratio = b / 12

However, since we do not have the value of "b," we cannot determine the exact common ratio without additional information.