Use summation notation to write the sum. $$- 3 - 6 - 12 - \ldots - 48$$
A) $\sum _ { n = 1 } ^ { 5 } - 3 ( 2 ) ^ { n - 1 }$
B) $\sum _ { n = 1 } ^ { 4 } - 3 ( 2 ) ^ { n + 1 }$
C) $\sum _ { n = 0 } ^ { 4 } - 3 ( 2 ) ^ { n - 1 }$
D) $\sum _ { n = 1 } ^ { 3 } - 3 ( 2 ) ^ { n }$
E) $\sum _ { n = 1 } ^ { 3 } - 3 ( 2 ) ^ { n - 1 }$

Question

Quizplus · Accepted Answer

The sequence is a geometric sequence with the first term $a = -3$ 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. The sequence goes from $-3$ to $-48$, which corresponds to $5$ terms ($-3, -6, -12, -24, -48$). Therefore, the summation notation that correctly represents this sum is $\sum _ { n = 1 } ^ { 5 } - 3 ( 2 ) ^ { n - 1 }$.

Use Summation Notation to Write the Sum −3−6−12−…−48- 3 - 6 - 12 - \ldots - 48−3−6−12−…−48

Use Summation Notation to Write the Sum $- 3 - 6 - 12 - \ldots - 48$