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