The given G.P is \( \sqrt{7}\), \( \sqrt{21}\), \(3 \sqrt{7}\), ….
Here,
a = \( \sqrt{7}\) and
r= \( \dfrac{\sqrt{21}}{\sqrt{7}}=\sqrt{3} \)
\( s_n=\dfrac{a(1-r^n)}{1-r}\)
\( \dfrac{\sqrt{7[1-(\sqrt{3})^n}]}{1-\sqrt{3}}\)
By rationalizing
\( \dfrac{\sqrt{7[1-(\sqrt{3})^n}]}{1-\sqrt{3}}\times\dfrac{1+\sqrt{3}}{1+\sqrt{3}}\)
\(\dfrac{\sqrt{7}(1+\sqrt{3})(1-\sqrt{3})^n)}{1-3}\)
\( \dfrac{\sqrt{7}(1+\sqrt{3})}{2}[(3)^\dfrac{n}{2}-1]\)
Answered by Pragya Singh | 1 year agoConstruct 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) a3b and ab3
(iii) –8 and –2
Insert 5 geometric means between \( \dfrac{32}{9}\) and \( \dfrac{81}{2}\).