Question 16Assume that $$(x+2)^{2017}+(x+2)^{2016}+\cdots+(x+2)^{2000}=a_{2017}x^{2017}+a_{2016}x^{2016}+\cdots+a_1x+a_0.$$ Find the value of the following expression: $$(a_0-a_1)+(a_2-a_3)+(a_4-a_5)+\cdots+(a_{2016}-a_{2017}).$$