Question

what is the sum of the geometric sequence 1, 3, 9, ... if there are 13 terms
a 123,201
b 164,268
c 797,161
d 818,573

Answer 1

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

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

$S_{13}= \frac{1(1-3^{13})}{1-3}$
$S_{13}= \frac{1-1594323}{-2}$
$S_{13}= \frac{-1594322}{-2}$
S13=797161

C is answer

Answer 2

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, $r = \frac{second term }{first term} = \frac{3}{1}$ = 3

Since, the sum of the geometric series,  

$S_n = \frac{a(r^n-1)}{r-1}$

⇒ $S_{13} = \frac{1 (3^{13}-1)}{3-1}$

⇒  $S_{13} = \frac{1594323-1}{3-1}$

⇒ $S_{13} = \frac{1594322}{2}$

⇒ $S_{13} = 797161$

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

Therefore, Option C is correct.