If 4÷3,m,1,n form a Gp what is the product of m and n
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So your terms of the GP are
4/3, m, 1, n
so a = 4/3
m = ar = (4/3)r
1 = ar^2 ----> 1 = 4/3 r^2
r^2 = 3/4
r = ± √3/2
then n = ar^3 = (4/3)(±√3/2)^3 = ± √3/2
m = ar = (4/3)(±√3/2) = ±√3
check:
4/3, √3, 1, √3/2 do form a GP, so does
4/3, -√3, 1, -√3
To determine the product of m and n in the given geometric progression (GP), we need to find the common ratio (r) first.
In a GP, the ratio between consecutive terms is always the same. So, we can compare the terms 4/3, m, 1, n to find the common ratio:
Common ratio (r) = (2nd term / 1st term) = (m / (4/3)) = m * (3/4)
Now, to find the product of m and n, we need to determine the value of r. To do this, we can compare the terms 1, m, n:
(r^2) = (3rd term / 2nd term) = (n / m)
Comparing the two expressions for the common ratio, we can equate them:
m * (3/4) = (n / m)
Multiply both sides by m:
3m^2 = 4n
Now, we can divide both sides by 3:
m^2 = (4n / 3)
Finally, to find the product of m and n, we need to solve for mn:
mn = (m * (4n / 3)) / m
mn = 4n / 3
Therefore, the product of m and n in the GP is 4n/3.
To determine the product of m and n, we need to identify the values of m and n first.
Given that 4, 3, 1, m, n form a geometric progression (GP), it means that each term is obtained by multiplying the preceding term by a common ratio.
Let's use the general form of a geometric progression to solve this:
The general form of a GP is: a, ar, ar^2, ar^3, ..., ar^(n-1)
In our case, the terms are 4, 3, 1, m, n. So, the common ratio (r) is obtained by dividing any term by the preceding term.
Let's find the common ratio by dividing each term by the preceding term:
3/4 = 1/3 = m/1 = n/m = r
Since the common ratio (r) is constant, we can equate any two of the ratios we found to find the values of m and n.
Using 3/4 = n/m, we can cross-multiply:
3m = 4n
To find the product of m and n (m * n), we need to solve this equation to find the specific values of m and n.
Dividing both sides by n:
(3m) / n = 4
Now, rearrange the equation to isolate the product of m and n:
m / n = 4/3
Multiply both sides by n:
m = (4/3) * n
So, the product of m and n is given by (4/3) * n.