The first term in a gemoetric series is 5 and the common ratio is 2 find the sum of the first 10 terms

5115

Step-by-step explanation:

We know:

a_1 = 5   the first term in the geometric sequence.

r = 2

We want  Sum a_i  for i = 1 to 10

a_n = 5* 2^(n-1)

Sum a_i for i = 1 to 10  =  G

G =  a_1* (2*2^(n-1) -  1)  /  (2 - 1)

G = 5 * (2^(n)  - 1)/  (2 - 1),   n = 10

G = 5* (2^(10)  - 1)

G = 5*(1024 - 1)  = 5*(1023) = 5115

the simplified form is

step-by-step explanation:

we want to simplify the expression,

let us change the middle bar to a normal division sign to obtain,

we multiply the first fraction by the reciprocal of the second fraction to obtain,

we factor to obtain,

we cancel the common factors to get,

we simplify to get,

the correct answer is b