Geometric:
[tex]a_n=Da_{n-1}=D^2a_{n-2}=\cdots=D^{n-1}a_1=D^{n-1}A[/tex]
The sum of the first 100 terms is
[tex]\displaystyle\sum_{n=1}^{100}D^{n-1}A=A\dfrac{1-D^100}{1-D}[/tex]
Arithmetic:
[tex]a_n=a_{n-1}+D=a_{n-2}+2D=\cdots=a_1+(n-1)D=A+(n-1)D[/tex]
The sum of the first 100 terms is
[tex]\displaystyle\sum_{n=1}^{100}(A+(n-1)D)=100A+\dfrac{99\times100}2D=100A+4950D[/tex]
