Question

How many terms of the G.P 3 , 3/2,3/4 are needed to give the Sum 3069 /512​

Answer 1

Answer: 10

Explanation:

The first term is 3 and the common ratio is 1/2.

Using the sum of a geometric series formula,

`(3069)/(512)=(3(1-(1/2)^(n))/(1-(1/2))\\\\(3069)/(1024)=3(1-(1/2)^(n))\\\\(1023)/(1024)=1-(1/2)^(n)\\\\-(1/2)^(n)=-(1)/(1024)\\\\(1/2)^n=\frac{1}[1024}\\\\2^(-n)=2^(-10)\\\\n=10`