Use summation notation to write the sum.? $$12 + 36 + 108 + \ldots + 8,748$$ ?
A) $$\sum _ { n = 1 } ^ { 7 } 12 ( 3 ) ^ { n - 1 }$$
B) $$\sum _ { n = 1 } ^ { 7 } 12 ( 3 ) ^ { n + 1 }$$
C) $\sum _ { n = 1 } ^ { 6 } 12 ( 3 ) ^ { n - 1 }$
D) $\sum _ { n = 1 } ^ { 7 } 3 ^ { n - 1 }$
E) $\sum _ { n = 1 } ^ { 7 } 12 ( 3 ) ^ { n }$

Question

Quizplus · Accepted Answer

The given series is a geometric series with the first term $a = 12$ and common ratio $r = 3$. The formula for the $n$th term of a geometric series is $a \cdot r^{n-1}$. The series starts with $12$ and multiplies by $3$ each time, which matches the formula in choice A, $12(3)^{n-1}$, for $n$ starting at $1$ and going up to $7$, indicating there are $7$ terms in the series.

Use Summation Notation to Write the Sum 12+36+108+…+8,74812 + 36 + 108 + \ldots + 8,74812+36+108+…+8,748

Use Summation Notation to Write the Sum $12 + 36 + 108 + \ldots + 8,748$