Express the Sum Using Summation Notation $$a + a r + a r ^ { 2 } + \ldots + a r ^ { 11 }$$

Multiple Choice

Express the sum using summation notation. Use a lower limit of summation not necessarily 1 and k for the index of summation.
- $$a + a r + a r ^ { 2 } + \ldots + a r ^ { 11 }$$

A) $\sum _ { \mathrm { k } = 0 } ^ { 11 } \mathrm { ar } ^ { \mathrm { k } }$
B) $\sum _ { k = 1 } ^ { 12 } a r ^ { k }$
C) $\sum _ { \mathrm { k } = 0 } ^ { 11 } ( \mathrm { ar } ) ^ { \mathrm { k } }$
D) $\sum _ { k = 1 } ^ { 11 } a r ^ { k }$