stevienicole27
stevienicole27 stevienicole27
  • 16-10-2021
  • Mathematics
contestada

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

Respuesta :

mariambarakat007
mariambarakat007 mariambarakat007
  • 16-10-2021

Answer:

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

Step-by-step explanation:

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