Express the sum using summation notation. Use 1 as the lower limit of summation and i for the index of summation.
-$$a + a r + a r ^ { 2 } + \ldots + a r ^ { 14 }$$
A) $\sum _ { \mathrm { i } = 1 } ^ { 14 } a r ^ { \mathrm { i } }$
B) $\sum _ { \mathrm { i } = 1 } ^ { 14 } ( \mathrm { ar } ) ^ { \mathrm { i } }$
C) $\sum _ { i = 1 } ^ { 15 } a r ^ { i-1 } $
D) $\sum _ { \mathrm { i } = 1 } ^ { 14 } ( \mathrm { ar } ) ^ { \mathrm { i } - 1 }$

Question

Quizplus · Accepted Answer

The given series is a geometric series starting from $a$ (which is $ar^0$) and ending at $ar^{14}$. To express it using summation notation starting from 1, we adjust the exponent to $i-1$, so the correct notation is $\sum _ { i = 1 } ^ { 15 } a r ^ { i-1 }$, which matches option C.

Express the Sum Using Summation Notation a+ar+ar2+…+ar14a + a r + a r ^ { 2 } + \ldots + a r ^ { 14 }a+ar+ar2+…+ar14

Express the Sum Using Summation Notation $a + a r + a r ^ { 2 } + \ldots + a r ^ { 14 }$