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 geometric with the first term $a = 2$ and common ratio $r = -3$. The formula for the $n$th term of a geometric sequence is $a \cdot r^{n-1}$. The sequence ends at $-486$, which is $2 \cdot (-3)^5$, indicating there are 6 terms. Therefore, the correct summation notation is $\sum _ { n = 1 } ^ { 6 } 2 ( - 3 ) ^ { n - 1 }$.

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 $2 - 6 + 18 - \ldots - 486$