Use the Formula for the Sum of the First n Terms of a Geometric Sequence
-Find the sum of the first 11 terms of the geometric sequence: $\frac { 1 } { 2 } , 1,2,4,8 , \ldots$
A) $\frac { 2047 } { 2 }$
B) $\frac { 2045 } { 2 }$
C) 1027
D) $\frac { 2041 } { 2 }$

Question

Quizplus · Accepted Answer

The sum of the first n terms of a geometric sequence is given by $S_n = \frac{a(1 - r^n)}{1 - r}$, where $a$ is the first term, $r$ is the common ratio, and $n$ is the number of terms. Here, $a = \frac{1}{2}$, $r = 2$, and $n = 11$. Plugging these values into the formula gives $S_{11} = \frac{\frac{1}{2}(1 - 2^{11})}{1 - 2} = \frac{\frac{1}{2}(1 - 2048)}{-1} = \frac{2047}{2}$.

Use the Formula for the Sum of the First N 12,1,2,4,8,…\frac { 1 } { 2 } , 1,2,4,8 , \ldots21​,1,2,4,8,…

Use the Formula for the Sum of the First N $\frac { 1 } { 2 } , 1,2,4,8 , \ldots$