Question
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
and 243/18, what is their common ratio?
A. 2.48
B. 3.68
C. 4.98
D. 1.18
Answers
Bot
Let's assume that the common ratio of the GP is "r".
The second term of the GP is given as 7, so we can write the second term as:
7 = a * r^(2-1)
7 = a * r
Similarly, the sixth term of the GP is given as 243/18, so we can write the sixth term as:
243/18 = a * r^(6-1)
243/18 = a * r^5
Dividing the equations, we get:
(243/18)/(7) = (a * r^5) / (a * r)
243/126 = r^4
Taking the fourth root on both sides, we get:
(r^4)^(1/4) = (243/126)^(1/4)
r = (243/126)^(1/4)
r ≈ 1.18
Therefore, the common ratio is approximately 1.18, so the answer is D. 1.18.
The second term of the GP is given as 7, so we can write the second term as:
7 = a * r^(2-1)
7 = a * r
Similarly, the sixth term of the GP is given as 243/18, so we can write the sixth term as:
243/18 = a * r^(6-1)
243/18 = a * r^5
Dividing the equations, we get:
(243/18)/(7) = (a * r^5) / (a * r)
243/126 = r^4
Taking the fourth root on both sides, we get:
(r^4)^(1/4) = (243/126)^(1/4)
r = (243/126)^(1/4)
r ≈ 1.18
Therefore, the common ratio is approximately 1.18, so the answer is D. 1.18.