jackelintinoco3 jackelintinoco3

17-05-2020
Mathematics

contestada

What is the sum of the geometric series 2+6+18+...+486?

Respuesta :

surjithayer10 surjithayer10

17-05-2020

Answer:

728

Step-by-step explanation:

2+6+18+...+486

a=2

r=6/2=3

[tex]a_{n}=ar^{n-1}\\486=2(3)^{n-1}\\3^{n-1}=486/2=243=3^5\\n-1=5\\n=5+1=6\\S_{6}=2\frac{3^6-1}{3-1} \\=2\frac{729-1}{2}\\=728[/tex]

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