The six terms of a G. P is 20 and the 12th term is 160. Find the common ratio

Answer 1

Let the first term of the G. P be a and the common ratio be r.
We know that the sixth term is 20, so we can write:
a * r^5 = 20 ......(1)
We also know that the twelfth term is 160, so we can write:
a * r^11 = 160 ......(2)
To find the value of r, we divide equation (2) by equation (1):
(r^11) / (r^5) = 160 / 20
r^6 = 8
Taking the sixth root on both sides:
r = ∛(8) = 2
Therefore, the common ratio is 2.