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

Question

Quizplus · Accepted Answer

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 $r \neq 1$. Plugging in the values, we get $S_7 = 5 \frac{1-3^7}{1-3} = 5 \frac{1-2187}{-2} = 5 \cdot 1093 = 5465$.

Find the N Th Partial Sum of the Geometric Sequence 5,15,45,135,405,…,n=75,15,45,135,405, \ldots, \quad n=75,15,45,135,405,…,n=7

Find the N Th Partial Sum of the Geometric Sequence $5,15,45,135,405, \ldots, \quad n=7$