Let's denote the common ratio of the geometric progression as 'r' and the first term as 'a'.
We know that the third term is 9/2, so we can express it as:
a * r^2 = 9/2
Similarly, the fifth term is 81/8, so we can express it as:
a * r^4 = 81/8
To solve this system of equations, let's first rewrite the fractions with a common denominator:
a * r^2 = 36/8
a * r^4 = 81/8
Next, let's simplify the equations:
a * r^2 = 9/2
a * r^4 = 9
Now, let's divide the second equation by the first equation to eliminate 'a':
(a * r^4) / (a * r^2) = 9 / (9/2)
r^2 = 2
Taking the square root of both sides, we find:
r = √2
Now, let's substitute the value of 'r' into one of the original equations to solve for 'a'. Using the third equation:
a * r^2 = 9/2
a * (√2)^2 = 9/2
a * 2 = 9/2
a = (9/2) / 2
a = 9/4
Therefore, the common ratio is √2 and the first term is 9/4.
The third and fifth terms of a geometric progression are 9/2 and 81/8 respectively, find the common ratio and first term
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