Given:

Sum of G.P = \(\dfrac{ 3069}{512}\)

Where, a = 3, r =\( \dfrac{ \dfrac{3}{2}}{3} = \dfrac{1}{2}\), n = ?

By using the formula,

Sum of GP for n terms =

\( \dfrac{ 3069}{512}\)= \(\dfrac{ 3( 9\dfrac{1}{2})n – 1)}{ (\dfrac{1}{2} – 1)}\)

\( \dfrac{ 3069}{512}×3×2 =\) \( 1- (\dfrac{1}{2})^n\)

\( \dfrac{ 3069}{3072}– 1=\) \( – (\dfrac{1}{2})^n\)

\(\dfrac{ (3069 – 3072)}{3072} = – (\dfrac{1}{2})^n\)

10 = n

10 terms are required to make \( \dfrac{ 3069}{512}\)

Answered by Sakshi | 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) **a^{3}b and ab^{3}

**(iii) **–8 and –2

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