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According to the given condition,

$a_{5}=ar_{5−1}=ar_{4}=p...(1)a_{8}=ar_{8−1}=ar_{7}=q...(2)a_{11}=ar_{11−1}=ar_{10}=s...(3)$

Dividing equation (2) by (1), we obtain

$ar_{4}ar_{7} =pq ⇒r_{3}=pq ....(4)$

Dividing equation (3) by (2), we obtain

$ar_{7}ar_{10} =qs ⇒r_{3}=qs ....(5)$

From (4) and (5) we obtain

$pq =qs ⇒q_{2}=ps$

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