We will have the following:
*First: We know that arithmetic sequences follow:
[tex]a_n=a_1+d(n-1)[/tex]*Second: From the information given we will have:
a100:
[tex]13=a_1+d(100-1)\Rightarrow13=a_1+99d[/tex]a200:
[tex]82=a_1+d(200-1)\Rightarrow82=a_1+199d[/tex]Then we will find the common difference:
[tex]d=\frac{82-13}{200-100}\Rightarrow d=\frac{69}{100}\Rightarrow d=0.69[/tex]So, the common difference is 0.69.
*Third: We determine the first term:
[tex]13=a_1+0.69(99)\Rightarrow_{}13=a_1+68.31[/tex][tex]\Rightarrow a_1=-55.31\Rightarrow a_1=-\frac{5531}{100}[/tex]So, the first term is -55.31.
