The common ratio of the G.P., r = 2

And, let a be the first term of the G.P.

Now,

a_{8} = ar ^{8–1} = ar^{7}

ar^{7} = 192

a(2)^{7} = 192

a(2)^{7} = (2)^{6} (3)

\( a=\dfrac{(2)^6\times 3}{(2)^7}=\dfrac{3}{2}\)

\( a_{12} = ar ^{12–1} = \dfrac{3(2)}{2}^{11}\)

(3)(2)^{10}= 3072

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

Find the geometric means of the following pairs of numbers:

**(i) **2 and 8

**(ii) **a^{3}b and ab^{3}

**(iii) **–8 and –2

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