The product of three consecutive terms of at G.P is 64 and the first term is four time the third. find the terms
t * r t * r^2 t = 64
t = 4 * r^2 t
so
r^2 = 1/4
r = 1/2
t + (1/2)t + (1/4) t = 64
etc
r = 1/2
t * t/2 * t/4 = 64
t^3/8 = 64
...
To find the terms of a geometric progression (G.P), we are given that the product of three consecutive terms is 64. Let's denote the terms as a, ar, and ar^2, where 'a' is the first term, 'r' is the common ratio, and ar^2 is the third term.
Given that the first term is four times the third term, we have the equation:
a = 4(ar^2)
Since we also know that the product of the three terms is 64, we can write the equation as:
a * ar * ar^2 = 64
Substituting a = 4(ar^2) into the second equation, we obtain:
4(ar^2) * ar * ar^2 = 64
Simplifying the equation:
4a^3r^5 = 64
Dividing both sides of the equation by 4:
a^3r^5 = 16
Now, we need to find the values of 'a' and 'r' such that a^3r^5 = 16.
One possible solution is when a = 2 and r = 2. Let's verify if this satisfies the given conditions.
For a = 2 and r = 2, the terms of the G.P are:
First term (a): 2
Second term (ar): 2 * 2 = 4
Third term (ar^2): 2 * 2^2 = 8
The product of the three terms is:
2 * 4 * 8 = 64
Hence, the terms of the G.P are 2, 4, and 8.