Question

If a, b, c are p^th, q^th and r^th terms respectively of G.P, then prove that

\(\begin{vmatrix} log\ a & p & 1\\ log\ b & q & 1 \\ log\ c & r & 1\end{vmatrix}\) = 0

Answer 1

Let A be the first term and R be the common ratio of the G.P. Then, we have

a = AR^{p - 1}

⇒ log a = log A + (p - 1) log R

b = AR^{q - 1}

⇒ log b = log A + (q - 1) log R

c = AR^{r - 1}

⇒ log c = log A + (r - 1) log R