Question

How many terms of the G.P. 3, 3/2, 3/4...... are needed to give the sum 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 = \(\frac{a(r^n-1)}{r-1}\)

∴ n = 10.