momoec momoec
  • 11-05-2019
  • Mathematics
contestada

What is the sum of the geometric sequence 4, 16, 64, ... if there are 8 terms? (6 points)

Respuesta :

jimrgrant1 jimrgrant1
  • 11-05-2019

Answer:

87380

Step-by-step explanation:

The sum to n terms of a geometric sequence is

[tex]S_{n}[/tex] = [tex]\frac{a(r^n-1)}{r-1}[/tex]

where a is the first term and r the common ratio

r = [tex]\frac{16}{4}[/tex] = 4 and a = 4, hence

[tex]S_{8}[/tex] = [tex]\frac{4(4^8-1)}{4-1}[/tex] = [tex]\frac{4(65535)}{4}[/tex] = 87380

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