Respuesta :

sum of geometric sequence where firts term is a1 andthe common ratio is r and the term you are summing to is n is

[tex]S_n= \frac{a_1(1-r^n)}{1-r} [/tex]
first term is 1
1 times 3=3
3 times 3=9
common ratio=3=r
13 terms, n=13

[tex]S_{13}= \frac{1(1-3^{13})}{1-3} [/tex]
[tex]S_{13}= \frac{1-1594323}{-2} [/tex]
[tex]S_{13}= \frac{-1594322}{-2} [/tex]
S13=797161

C is answer

Answer: c. 797161

Step-by-step explanation:

Here, the given geometric sequence,

1, 3, 9, ...    

And, total number of the terms , n = 13.

first term, a = 1, and the common ratio, [tex]r = \frac{second term }{first term} = \frac{3}{1}[/tex] = 3

Since, the sum of the geometric series,  

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

⇒ [tex]S_{13} = \frac{1 (3^{13}-1)}{3-1}[/tex]

⇒  [tex]S_{13} = \frac{1594323-1}{3-1}[/tex]

⇒ [tex]S_{13} = \frac{1594322}{2}[/tex]

⇒ [tex]S_{13} = 797161[/tex]

Thus, the sum of the given geometric series is 797161.

Therefore, Option C is correct.

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