If a1,a2,…,an,… form a G.P. and ai > 0, for all i≥1, then logan logan+1 logan+2logan+3 logan+4 logan+5logan+6 logan+7 logan+8 is equal to
0
1
2
3
We have,
an+12=anan+2
⇒ 2log an+1=log an+log an+2
Similarly,
2logan+4=logan+3+logan+52logan+7=logan+6+logan+8
Substituting these values in second column of determinant, we get
Δ=12loganlogan+logan+2logan+2logan+3logan+3+logan+5logan+5logan+6logn+6+logan+8logan+8=12(0)=0 [Using C2→C2−C1−C3