Find the n th partial sum of the geometric sequence. $\ldots, \quad n=7$

A) 1,820
B) 5,465
C) 200
D) 5,514
E) 5,808

Question

Find the n th partial sum of the geometric sequence.  5,15,45,135,405, \ldots, \quad n=7  A)1,820 B)5,465 C)200 D)5,514 E)5,808

Abbey Marshall · Accepted Answer

Final Answer : B, Explanation :   The given sequence is a geometric sequence with the first term  a = 5  and common ratio  r = 3 . The nth partial sum of a geometric sequence is given by  S_n = a \frac{1-r^n}{1-r}  for  r 
eq 1 . Plugging in the values, we get  S_7 = 5 \frac{1-3^7}{1-3} = 5 \frac{1-2187}{-2} = 5 \cdot 1093 = 5465 .

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