Write the sum using summation notation.
-$$a + a r + a r ^ { 2 } + a r ^ { 3 } + \ldots + a r ^ { 19 }$$
A) $\sum _ { i = 1 } ^ { 19 } a r ^ { j - 1 }$
B) $\sum _ { i = 1 } ^ { 20 } a r ^ { i - 1 }$
C) $\sum _ { i = 1 } ^ { 19 } a r ^ { i }$
D) $\sum _ { i = 1 } ^ { 20 } a r ^ { i }$

Question

Quizplus · Accepted Answer

The series starts with $a$, which can be represented as $a r^{0}$, and goes up to $a r^{19}$. The summation notation that correctly represents this is $\sum _ { i = 1 } ^ { 20 } a r ^ { i - 1 }$, where $i$ starts from 1 and goes to 20, and $i-1$ correctly adjusts the exponent to start from 0 up to 19.

Write the Sum Using Summation Notation a+ar+ar2+ar3+…+ar19a + a r + a r ^ { 2 } + a r ^ { 3 } + \ldots + a r ^ { 19 }a+ar+ar2+ar3+…+ar19

Write the Sum Using Summation Notation $a + a r + a r ^ { 2 } + a r ^ { 3 } + \ldots + a r ^ { 19 }$