Use the Formula for the Sum of the First n Terms of a Geometric Sequence
-Find the sum of the first five terms of the geometric sequence: $\frac { 3 } { 3 } , \frac { 3 } { 6 } , \frac { 3 } { 12 } , \ldots .$
A) $\frac { 31 } { 16 }$
B) $\frac { 1 } { 24 }$
C) 93
D) $- \frac { 1 } { 12 }$

Question

Quizplus · Accepted Answer

The sum of the first five terms of a geometric sequence can be found using the formula $S_n = \frac{a(1 - r^n)}{1 - r}$, where $a$ is the first term, $r$ is the common ratio, and $n$ is the number of terms. Here, $a = \frac{3}{3} = 1$, $r = \frac{3/6}{3/3} = \frac{1}{2}$, and $n = 5$. Plugging these values into the formula gives $S_5 = \frac{1(1 - (\frac{1}{2})^5)}{1 - \frac{1}{2}} = \frac{1 - \frac{1}{32}}{\frac{1}{2}} = \frac{31}{32} \times 2 = \frac{31}{16}$.

Use the Formula for the Sum of the First N 33,36,312,….\frac { 3 } { 3 } , \frac { 3 } { 6 } , \frac { 3 } { 12 } , \ldots .33​,63​,123​,….

Use the Formula for the Sum of the First N $\frac { 3 } { 3 } , \frac { 3 } { 6 } , \frac { 3 } { 12 } , \ldots .$