Question

What is the sum of the first eight terms of a geometric series whose first term is 3 and whose comman ratio is 1/2

Answer 1

there is a formula...

Sn = a1 (1 - r^n) / (1 - r)

a1 = first term = 3

n = number of terms = 8

r = common ratio = 1/2

now we sub

S(8) = 3(1 - 1/2^8) / (1 - 1/2)

S(8) = 3(1 - (1/2^8) / (1/2)

S(8) = 3(1 - 1/256) / (1/2)

S(8) = 3 (256/256 - 1/256) / (1/2)

S(8) = 3(255/256) / (1/2)

S(8) = (765/256) / (1/2)

S(8) = 765/256 * 2/1

S(8) = 1530/256

S(8) = 765/128 or 5 125/128 or 5.9765625

Explanation: