Let's denote the second term of the geometric progression as a and the common ratio as r. We know that the second term, a, is equal to 7, and the sixth term is equal to (243/18).
The formula for the nth term of a geometric progression is given by:
Tn = ar^(n-1)
We can set up two equations using the given information:
7 = a * r^(2-1) => 7 = a * r
(243/18) = a * r^(6-1) => (243/18) = a * r^5
Dividing the second equation by the first equation, we can eliminate the term a:
(243/18) / 7 = (a * r^5) / (a * r)
(243/18) / 7 = r^4
(243/18) / 7 = r^(4-1)
(243/18) / 7 = r^3
Simplifying the left-hand side of the equation: 243/18 divided by 7 equals (243/18)*(1/7) = 243/126
243/126 = r^3
Taking the cube root of both sides of the equation, we get:
(r^3)^(1/3) = (243/126)^(1/3)
r = (243/126)^(1/3)
Calculating the cube root of (243/126) using a calculator, we find that r ≈ 1.179535.
Therefore, the common ratio of the geometric progression is approximately 1.18.
The correct answer is D. 1.18.
The second and sixth terms of a G.P are 7
and 243/18, what is their common ratio?
A. 2.48
B. 3.68
C. 4.98
D. 1.18
1 answer