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
[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.