Find the sum of the first 20 terms of a geometric sequence which has a first term of 5 and a common ratio of 2?

Question

help ASAP!!!!

Answer 1

Brianna,

 

The formula for the sum of the first n terms of a geometric sequence is:

 

∑a_i = a((1-rⁿ)/(1-r))  ; i = 1 should be below the sigma, and n should be above the sigma, where i is the index starting at position 1, and n is the number of terms you want to sum to, a is the first term:

 

So, the sum of the first 20 terms:

 

5((1-2²⁰)/(1-2))

5(1-1048576)/-1

5(-1048575)/-1

5(1048575)

5242875

So, the sum of the first 20 terms with a first term of 5 and a common ratio of 2 is 5242875