Geometric Progression Assignment Solutions

Problem 1

Problem 1

A geometric progression is a sequence of numbers where the quotient of adjacent terms is constant (common ratio). Any term in the sequence is given by the equation: 

li = a r (i - 1) , for i = 1, 2, 3, . . . 

where a is the first term and r is known as the common ratio.

a) Write a computer program in Mathcad, using a for loop, to determine and display the first n terms in a geometric series for any values of first term and common ratio.

b) Use your program to display the first 15 numbers of the geometric sequence with a = 9 and r = 2/3. 

Problem 2

The sum of a geometric progression converge to a finite number when the common ratio is less than 1. This is because the terms tend to zero as the number of terms increases. 

a) Write a program in Mathcad, using a for loop, to determine the sum of the first n terms in a geometric series for any values of first term and common ratio.  

b) Using a = 9 and r = 2/3, show that as you increase the number of terms the sum converges to a/1(1-r)