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