Consider a geometric progression (GP) whose first term is and common ratio is

MATHEMATICS · Multi-part · A Level · Mathematics · Sequences and series · Sequences and series

Problem

Consider a geometric progression (GP) whose first term is

a

and common ratio is

r\,(\neq 0)

. Every term of this progression is multiplied by a non–zero constant

k

to form a new progression. (i) Write the first term and the common ratio of the new progression. (ii) Prove that the

n

th term of the new progression is

k

times the

n

th term of the original progression. (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.