If 4/3, m, ,1,n form a Gp the product of m and n is
Assuming that ", ," is a typo,
r^2 = 3/4
mn = (4/3 * r) * (4/3 * r^3) = 16/9 r^4 = 16/9 * 9/16 = 1
If there is a missing term there, then adjust the powers of r.
To determine the product of m and n in the given geometric progression (GP), we need to find the common ratio.
The general formula for the nth term of a GP is given by:
an = a*r^(n-1),
where an represents the nth term, a is the first term, r is the common ratio, and n is the position of the term in the progression.
In the given GP, the first term (a) is 4/3. Let's assume m is the second term, so m = a*r = (4/3)*r.
The third term is 1, so n = a*r^2 = (4/3)*r^2.
Since these three terms form a GP, we can equate the ratios:
(m/a) = (n/m).
Substituting the values, we get:
[(4/3)*r] / (4/3) = [(4/3)*r^2] / (4/3)*r.
Simplifying the equation, we obtain:
r = r^2.
Dividing both sides by r, we have:
1 = r.
So, the common ratio (r) is 1.
Now, substituting the values of a and r into the formulas for m and n, we get:
m = (4/3)*1 = 4/3,
n = (4/3)*1^2 = 4/3.
Therefore, the product of m and n is:
m * n = (4/3) * (4/3) = 16/9.
Thus, the product of m and n in the given GP is 16/9.
To determine the product of m and n in the given geometric progression (GP), we need to find the value of m and n.
Let's recall the definition of a geometric progression (GP). In a GP, each term is obtained by multiplying the previous term by a constant ratio. In this case, we are given four terms: 4/3, m, 1, and n.
We start by finding the common ratio (r) of the GP. To do this, we divide each term by its previous term:
m/(4/3) = (4/3)/1 = 4/3
1/m = m/(4/3) = 4/3
n/1 = 1/m = 4/3
Now, by comparing the ratios above, we see that all three ratios are equal to 4/3. Hence, the common ratio (r) of the GP is 4/3.
To find m and n, we multiply each term by the common ratio:
m = (4/3) * (4/3) = 16/9
n = (1) * (4/3) = 4/3
Finally, to find the product of m and n, we multiply their values:
m * n = (16/9) * (4/3) = 64/27
Therefore, the product of m and n in the given GP is 64/27.