Consider a geometric progression (GP) whose first term is a and common ratio is r(=0). Every term of this progression is multiplied by a non–zero constant k to form a new progression.
a. (i) Write the first term and the common ratio of the new progression.
b. (ii) Prove that the nth term of the new progression is k times the nth term of the original progression.
c. (iii) Show that the sum of the first n terms of the new progression equals k times the sum of the first n terms of the original progression.