If a₁, a₂, a₃, , a_n, . are in G.P., then the value of the determinant | array ccc a_n & a_ n+1 & a_ n+2 a_ n+3 & a_ n+4 & a_ n+5 a_ n+6 & a_ n+7 & a_ n+8 array | , is

Step-by-step solution

aligned & | array lll a_n & a_ n+1 & a_ n+2 a_ n+3 & a_ n+4 & a_ n+5 a_ n+6 & a_ n+7 & a_ n+8 array | & C₃ C₃-C₂, C₂ C₃-C₁ & = | array lll a_n & r & r a_ n+3 & r & r a_ n+6 & r & r array |=0 aligned (where r is a common ratio).