According to the conditions given in the question,
\( s_1=\dfrac{n(n+1)}{2} \)
\( s_3=\dfrac{n^2(n+1)^2}{4} \)
Therefore,
= \( s_3(1+8s_1)=\dfrac{n^2(n+1)^2}{4} \)
\( [1+\dfrac{8n(n+1)}{2}]\)
= \( \dfrac{n^2(n+1)^2}{4}[1+4n^2+4]\)
= \( \dfrac{n^2(n+1)^2}{4}(2n+1)^2\)
= \( \dfrac{[n(n+1)(2n+1)]^2}{4}\) .........(1)
And.
\( 9s^2_2=9 \dfrac{[n(n+1)(2n+1)]^2}{(6)^2} \)
= \(\dfrac{9}{36}[n+(n+1)(2n+1)]^2 \)
\(= \dfrac{[n(n+1)(2n+1)]^2}{4}\) .............(2)
Therefore, we get
\( 9s^2_2= s_3(1+8s_1)\) from (1) and (2).
Answered by Abhisek | 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 \( \dfrac{81}{2}\).