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

Step-by-step explanation:

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

Using the sum of a geometric series formula,

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