Use summation notation to write the sum. $8 + 16 + 32 + \ldots + 1024$
A) $\sum _ { n = 1 } ^ { 8 } 8 ( 2 ) ^ { n + 1 }$
B) $\sum _ { n = 1 } ^ { 8 } 8 ( 2 ) ^ { n - 1 }$
C) $\sum _ { n = 1 } ^ { 8 } 8 ( 2 ) ^ { n }$
D) $\sum _ { n = 1 } ^ { 7 } 8 ( 2 ) ^ { n - 1 }$
E) $\sum _ { n = 1 } ^ { 8 } ( 2 ) ^ { n - 1 }$

Question

Use summation notation to write the sum.   $8 + 16 + 32 + \ldots + 1024$  
A) $\sum _ { n = 1 } ^ { 8 } 8 ( 2 ) ^ { n + 1 }$
B) $\sum _ { n = 1 } ^ { 8 } 8 ( 2 ) ^ { n - 1 }$
C) $\sum _ { n = 1 } ^ { 8 } 8 ( 2 ) ^ { n }$
D) $\sum _ { n = 1 } ^ { 7 } 8 ( 2 ) ^ { n - 1 }$
E) $\sum _ { n = 1 } ^ { 8 } ( 2 ) ^ { n - 1 }$

Quizplus · Accepted Answer

The sequence is a geometric series with the first term $a = 8$ and common ratio $r = 2$. The nth term of a geometric series can be written as $a \cdot r^{n-1}$, where $n$ is the term number. Therefore, the correct expression is $\sum _ { n = 1 } ^ { 8 } 8 ( 2 ) ^ { n - 1 }$.

Use Summation Notation to Write the Sum 8+16+32+…+10248 + 16 + 32 + \ldots + 10248+16+32+…+1024

Use Summation Notation to Write the Sum $8 + 16 + 32 + \ldots + 1024$