​ How many terms of the G.P. 3, 3/2,3/4 . Be taken together to make 3069/512 ? ​

Question

How many terms of the G.P. 3,\(\frac{3}{2}\), \(\frac{3}{4}\). Be taken together to make \(\frac{3069}{512}\)?

Answer 1

Given: 

Sum of GP = \(\frac{3069}{512}\)

 ∴ Common Ratio = r = \(\cfrac{\frac{3}{2}}{3}\) = \(\frac{1}{2}\)

a = 3 

To find: Number of terms = n.

Sum of GP for n terms = \(\frac{a(r^n-1)}{(r-1)}\)

\(\therefore n = 10\)