Consider a geometric progression whose first term is (a ) and common ratio (r 1 ).

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

Problem

Consider a geometric progression whose first term is

a

and common ratio

r\neq1

. (i) Show that

\dfrac{a_p\,a_q}{a_r\,a_s}=r^{\,(p+q)-(r+s)}

. (ii) Using the result of part (i), find the common ratio when

a_2\,a_{11}=32\,a_5\,a_7