Question

Construct a Geometric and Arithmetric sequence which has a first term A and common difference D with 1000terms. calculate the sum of first 100 terms

Answer 1

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(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+\frac{99*100}2D=100A+4950D`