Use summation notation to write the sum. $4 - 8 + 16 - K + 64$
A) $\sum _ { n = 0 } ^ { 4 } 4 ( - 2 ) ^ { n - 1 }$
B) $\sum _ { n = 1 } ^ { 3 } 4 ( - 2 ) ^ { n }$
C) $\sum _ { n = 1 } ^ { 5 } 4 ( - 2 ) ^ { n - 1 }$
D) $\sum _ { n = 1 } ^ { 3 } 4 ( - 2 ) ^ { n - 1 }$
E) $\sum _ { n = 1 } ^ { 4 } 4 ( - 2 ) ^ { n + 1 }$

Question

Quizplus · Accepted Answer

The given sequence is a geometric sequence with the first term $a = 4$ and common ratio $r = -2$. The general term of a geometric sequence is given by $a \cdot r^{n-1}$, where $n$ is the term number. Therefore, the sum can be represented as $\sum _ { n = 1 } ^ { 5 } 4 ( - 2 ) ^ { n - 1 }$, which matches option C.

Use Summation Notation to Write the Sum 4−8+16−K+644 - 8 + 16 - K + 644−8+16−K+64

Use Summation Notation to Write the Sum $4 - 8 + 16 - K + 64$