Express the Sum Using Summation Notation $$15 + 19 + 23 + 27 + \ldots + 47$$

Express the sum using summation notation. Use a lower limit of summation, not necessarily 1, and k for the index of summation.
- $$15 + 19 + 23 + 27 + \ldots + 47$$

A) $\sum _ { k = 2 } ^ { 10 } 4 k + 7$
B) $\sum _ { k = 1 } ^ { 10 } 4 k + 7$
C) $\sum _ { k = 0 } ^ { 32 } 4 k + 7$
D) $\sum _ { k = 2 } ^ { 32 } 4 k + 7$