3 geometric means between 32 and 1/8
There is only one geometric mean between two numbers. In this case it is sqrt[(32*(1/8)] = 2.
If you want three intermediate numbers in a geometric series between 1/8 and 32, the series would be
1/8, 1/2, 2, 8, 32.
Each number is four times the previous number in the series.
Find 3 geometric means between 32 and ⅛
To find the three geometric means between 32 and 1/8, we need to find the common ratio between consecutive terms.
The formula for the geometric mean between two numbers, a and b, is the square root of their product, (√ab).
Given that the first term, a, is 32, and the last term, b, is 1/8, we can write the equation as follows:
√(32x)(x)(x)(1/8) = 1/8
Simplifying this equation:
√(32x^4/8) = 1/8
Simplifying the square root:
√(4x^4) = 1/8
Squaring both sides of the equation:
4x^4 = (1/8)^2
4x^4 = 1/64
Multiplying both sides by 64 to eliminate fractions:
256x^4 = 1
Dividing both sides by 256:
x^4 = 1/256
Taking the fourth root of both sides:
x = √(1/256)
x = 1/4
Therefore, the common ratio (x) between consecutive terms is 1/4.
To find the three geometric means, we multiply the previous term by the common ratio:
1/8 * 1/4 = 1/32
1/32 * 1/4 = 1/128
1/128 * 1/4 = 1/512
So, the three geometric means between 32 and 1/8 are 1/32, 1/128, and 1/512.
To find the 3 geometric means between 32 and 1/8, we need to first understand what a geometric mean is.
A geometric mean is the middle term between two numbers when they are in geometric progression. In other words, it is the number that, when multiplied by itself several times, gives you the second number when multiplied by the first number.
To find the geometric mean, we can use the formula:
Geometric mean = √(first number * second number)
Now, let's calculate the geometric means between 32 and 1/8.
Step 1: Find the first geometric mean
First number = 32
Second number = 1/8
Geometric mean = √(32 * 1/8) = √(4) = 2
So, the first geometric mean between 32 and 1/8 is 2.
Step 2: Find the second geometric mean
First number = 32
Second number = 2
Geometric mean = √(32 * 2) = √(64) = 8
So, the second geometric mean between 32 and 1/8 is 8.
Step 3: Find the third geometric mean
First number = 32
Second number = 8
Geometric mean = √(32 * 8) = √(256) = 16
So, the third geometric mean between 32 and 1/8 is 16.
Therefore, the 3 geometric means between 32 and 1/8 are 2, 8, and 16.