The third of geometric progression (G.P) is 10 and the sixth term is 80. Find the common ratio.
Answer Details
We can use the formula for the nth term of a geometric progression to solve this problem. Let a be the first term and r be the common ratio, then the third term is ar^2 and the sixth term is ar^5. We are given that ar^2 = 10 and ar^5 = 80.
Dividing the second equation by the first, we get:
(ar^5)/(ar^2) = 80/10
Simplifying and canceling a, we get:
r^3 = 8
Taking the cube root of both sides, we get:
r = 2
Therefore, the common ratio is 2, and the answer is (a) 2.