Question

If $2^{a_{1}}$, $2^{a_{2}}$,$2^{a_{3}}$..... $2^{a_{n}}$ are in G.P. Then

$\left| \begin{matrix} a_{1} & a_{2} & a_{3} \\ a_{n + 1} & a_{n + 2} & a_{n + 3} \\ a_{2n + 1} & a_{2n + 2} & a_{2n + 3} \end{matrix} \right|$ is equal to

• A. 2
• B. 2³
• C. 0
• D. None of these

Answer 1

Answer: (C)

0

Answer 2

$2^{a_{1}}$, $2^{a_{2}}$,$2^{a_{3}}$..... are in G.P Ž a₂ – a₁ = a₃ – a₂ = a₄ – a₃ =..... Ž a₁, a₂, a₃ ..... are in A.P.

Ž a_2n+1 + a₁ = 2a_n+1, a₂ + a_2n+2 = 2a_n+2, a₃ + a_2n+3 = 2a_n+3

Ž D = $\frac { 1 } { 2 }$ $\left| \begin{matrix} a_{1} & a_{2} & a_{3} \\ 0 & 0 & 0 \\ a_{2n + 1} & a_{2n + 2} & a_{2n + 3} \end{matrix} \right|$ = 0