Question

How many terms of the G.P. 3, `3/2`,`3/4``,dotdotdot`are needed to give the sum `(3069)/(512)`?

Answer 1

Here, `a = 3 and r = 1/2`
`S_n = (a(1-r^n))/(1-r)`
`3069/512 = (3(1-(1/2)^n))/(1-(1/2))`
`1023/1024= 1-(1/2)^n`
`(1/2)^n = 1/1024=(1/2)^10`
So, `n = 10` is the required answer.