Show that progressions is a G.P. Also, find the common ratio 4, -2, 1, -1/2, 

Construct a quadratic in x such that A.M. of its roots is A and G.M. is G.

Find the two numbers whose A.M. is 25 and GM is 20.

If a is the G.M. of 2 and \( \dfrac{1}{4}\) find a.

Find the geometric means of the following pairs of numbers:

(i) 2 and 8

(ii) a³b and ab³

(iii) –8 and –2

Insert 5 geometric means between \( \dfrac{32}{9}\) and \( \dfrac{81}{2}\).