Find the sum of the finite geometric series

Question

3+6+12+...+768

Answer 1

The common ratio r = 2

Because each term is 2 times the previous... a_n = 2a_n-1

 

Let's find out how far into the series the term 768 is:

 

r = 2

a₁ = 3

 

a_n = 3(2^n-1)

 

768 = 3(2^n-1)

256 = 2^n-1

256 = 2⁸

n-1 = 8

n = 9

 

a₉ = 768

 

 

S_n=  a₁(1 - rⁿ)/(1 - r) where r is the common ratio

 

Sum = 3(1-2⁹)/(1-2) = 1533