3 years ago

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

Mathematics

1 answer:

marin [14]3 years ago

6 0

Answer:

728

Step-by-step explanation:

2+6+18+...+486

a=2

r=6/2=3

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

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