Answer
$$\sum\limits_{i = 1}^{15} {\left( { - 5i + 9} \right)} $$
Work Step by Step
$$\eqalign{
& 4 - 1 - 6 - \cdots - 66 \cr
& {\text{Calculating }}d{\text{ or }}r \cr
& - 1 - 4 = - 5 \cr
& - 6 - \left( { - 1} \right) = - 5 \cr
& {\text{This is an arithmetic series with }}{a_1} = 4{\text{ and }}d = - 5 \cr
& {\text{The general term is }} \cr
& {a_n} = {a_1} + \left( {n - 1} \right)d \cr
& {a_n} = 4 + \left( {n - 1} \right)\left( { - 5} \right) \cr
& {a_n} = 4 + \left( {n - 1} \right)\left( { - 5} \right) \cr
& {a_n} = 4 - 5n + 5 \cr
& {a_n} = - 5n + 9 \cr
& {\text{The last term is }} - 66,{\text{ then}} \cr
& - 66 = - 5n + 9 \cr
& n = 15 \cr
& {\text{The sum of notation can be written as}} \cr
& \sum\limits_{i = 1}^{15} {\left( { - 5i + 9} \right)} \cr} $$
