Let ((a_n) ) be a geometric progression with non–zero terms.

MATHEMATICS · Multi-part · CBSE · Mathematics · Sequences and Series · Sequences and Series

Problem

Let

(a_n)

be a geometric progression with non–zero terms. (i) Prove that for any positive integers

p

and

q

\dfrac{a_p}{a_q}=r^{\,p-q}

. (ii) Show that for any positive integer

k

a_{m-k}\,a_{m+k}=a_m^{\,2}

. (iii) Deduce the corresponding property for the first, last and equidistant terms of a finite geometric progression.