Use summation notation to write the sum.
$2 - 6 + 18 - \ldots - 486$
A) $\sum _ { n = 0 } ^ { 5 } 2 ( - 3 ) ^ { n - 1 }$
B) $\sum _ { n = 1 } ^ { 4 } 2 ( - 3 ) ^ { n }$
C) $\sum _ { n = 1 } ^ { 6 } 2 ( - 3 ) ^ { n - 1 }$
D) $\sum _ { n = 1 } ^ { 4 } 2 ( - 3 ) ^ { n - 1 }$
E) $\sum _ { n = 1 } ^ { 5 } 2 ( - 3 ) ^ { n + 1 }$

Question

Quizplus · Accepted Answer

The sequence is a geometric sequence with the first term $a = 2$ and common ratio $r = -3$. The nth term of a geometric sequence is given by $a \cdot r^{n-1}$. Thus, the summation notation that correctly represents the given sequence is $\sum _ { n = 1 } ^ { 6 } 2 ( - 3 ) ^ { n - 1 }$, since the last term $486$ corresponds to $2 \cdot (-3)^5$, indicating that the sequence goes up to $n = 6$.

Use Summation Notation to Write the Sum 2−6+18−…−4862 - 6 + 18 - \ldots - 4862−6+18−…−486

Use Summation Notation to Write the Sum $2 - 6 + 18 - \ldots - 486$