If a1,a2,…,an,… form a G.P.  then log⁡an       log⁡an+1    log⁡an+2log⁡an+3    log⁡an+4    log⁡an+5log⁡an+6    log⁡an+7    log⁡an+8 is equal to  =  , (where ai>0 ,   for all i≥1)

We have,an+12=anan+2⇒ 2log ⁡an+1=log ⁡an+log ⁡an+2Similarly,2log⁡an+4=log⁡an+3+log⁡an+52log⁡an+7=log⁡an+6+log⁡an+8Substituting these values in second column of determinant, we getΔ=12log⁡anlog⁡an+log⁡an+2log⁡an+2log⁡an+3log⁡an+3+log⁡an+5log⁡an+5log⁡an+6logn+6+log⁡an+8log⁡an+8=12(0)=0  [Using C2→C2−C1−C3