Find the sum of the geometric series.
-$$4 + 8 + 16 + 32 + 64 + \ldots + 4 \cdot 2 ^ { 9 }$$
A)4092
B)4094
C)4129
D)4072

Question

Quizplus · Accepted Answer

The sum of a geometric series can be calculated using the formula $$S_n = \frac{a(1 - r^n)}{1 - r}$$, where $S_n$ is the sum of the first $n$ terms, $a$ is the first term, $r$ is the common ratio, and $n$ is the number of terms. Here, $a = 4$, $r = 2$, and $n = 10$ (since $4 \cdot 2^9$ is the 10th term, starting from $4 \cdot 2^0$). Plugging these values into the formula gives $$S_{10} = \frac{4(1 - 2^{10})}{1 - 2} = \frac{4(-1023)}{-1} = 4092.$$

Find the Sum of the Geometric Series 4+8+16+32+64+…+4⋅294 + 8 + 16 + 32 + 64 + \ldots + 4 \cdot 2 ^ { 9 }4+8+16+32+64+…+4⋅29

Find the Sum of the Geometric Series $4 + 8 + 16 + 32 + 64 + \ldots + 4 \cdot 2 ^ { 9 }$