find the product of x and y if x,3/2,6/7,y are in geometric progression
T2=ar =3/2
T3=ar^2 =6/7
ar^2/ar=6/7/3/2
r=4/7
Recall T2=ar
3/2=4/7a
a=21/8
Therefore, x=21/8
T4(y) =ar^3
T4=21/8×(4/7)^3
T4=21/8×64/343
T4=24/49
Therefore y=24/49
Product=21/8 ×24/49
=9/7
r = (6/7) / (3/2) = 4/7
x = (3/2) * (7/4)
y = (6/7) * (4/7)
The third and fourth of a g.p are 48 and 142/9 respectively write down the first four terms
To find the product of x and y, we first need to determine the common ratio of the geometric progression.
In a geometric progression, each term is obtained by multiplying the previous term by a constant called the common ratio (r).
Given the terms x, 3/2, 6/7, and y, we can express the terms using the general formula for a geometric progression:
x = a
3/2 = a * r
6/7 = a * r^2
y = a * r^3
To find the common ratio (r), we can use the second and third terms:
3/2 = a * r
6/7 = a * r^2
We can solve for 'a' by dividing the second equation by the first equation:
(6/7)÷(3/2) = (a * r^2) / (a * r)
(6/7)÷(3/2) = r
Simplifying the equation gives us:
4/7 = r
Now that we know the common ratio (r), we can find the value of 'a' by substituting back into the first equation:
3/2 = a * (4/7)
To find 'a', we rearrange the equation:
a = (3/2) / (4/7)
a = (3/2) * (7/4)
a = 21/8
Now that we have the value of 'a', we can find the product of x and y:
x * y = (a) * (a * r^3)
x * y = (21/8) * [(21/8) * (4/7)^3]
Simplifying the expression gives us the product of x and y in terms of 'a' and 'r'.