Question

If a = 1 + 2 + 4 + ....... up to n terms b = 1 + 3 + 9 + ....... up to n terms and c = 1 + 5 + 25 + ......... up to n terms then ∆ = $\left| \begin{matrix} a & 2b & 4c \\ 2 & 2 & 2 \\ 2^{n} & 3^{n} & 5^{n} \end{matrix} \right|$ =

• A. (30)ⁿ
• B. (10)ⁿ
• C. 0
• D. 2ⁿ + 3ⁿ + 5ⁿ

Answer 1

Answer: (C)

0

Answer 2

a = 2ⁿ –1, 2b = 3ⁿ –1, 4c = 5ⁿ –1

∆ =2$\left| \begin{matrix} 2^{n}–1 & 3^{n}–1 & 5^{n}–1 \\ 1 & 1 & 1 \\ 2^{n} & 3^{n} & 5^{n} \end{matrix} \right|$= 2$\left| \begin{matrix} 2^{n} & 3^{n} & 5^{n} \\ 1 & 1 & 1 \\ 2^{n} & 3^{n} & 5^{n} \end{matrix} \right|$R₁→R₁+R₂ = 0