Use Summation Notation
-$a + a r + a r ^ { 2 } + \ldots + a r ^ { 14 }$
A) $\sum _ { \mathrm { k } = 0 } ^ { 14 } a \mathrm { r } ^ { \mathrm { k } }$
B) $\sum _ { \mathrm { k } = 1 } ^ { 15 } a \mathrm { r } ^ { \mathrm { k } }$
C) $\sum _ { \mathrm { k } = 0 } ^ { 14 } ( \mathrm { ar } ) ^ { \mathrm { k } }$
D) $\sum _ { k = 1 } ^ { 14 } a r ^ { k }$

Question

Quizplus · Accepted Answer

The given sequence is a geometric sequence with first term $a$ and common ratio $r$. Summation notation for a geometric sequence is $\sum _ { \mathrm { k } = 0 } ^ { n - 1 } a r ^ { \mathrm { k } }$ where $n$ is the number of terms. In this case, there are 15 terms (from $a$ to $ar^{14}$), so the correct summation notation is $\sum _ { \mathrm { k } = 0 } ^ { 14 } a \mathrm { r } ^ { \mathrm { k } }$. Choice A matches this notation.

Use Summation Notation - a+ar+ar2+…+ar14a + a r + a r ^ { 2 } + \ldots + a r ^ { 14 }a+ar+ar2+…+ar14

Use Summation Notation
- $a + a r + a r ^ { 2 } + \ldots + a r ^ { 14 }$