First slide

Geometric progression

Question

If $l, m, n$ are positive and are respectively the $p t h, q t h a n d r t h$ terms of a G.P., then
$Δ = |\begin{array}{lll} \log l p 1 \\ \log m q 1 \\ \log n r 1 \end{array}|$ is equal to

Moderate

A

$p q r$
B

$p + q + r$
C

$p + q + r + p q r$
D

0

Solution

$\begin{array}{l} l = A R^{p - 1}, m = A R^{q - 1}, n = A R^{r - 1} \\ Δ = |\begin{array}{lll} a + (p - 1) d & p & 1 \\ a + (q - 1) d & q & 1 \\ a + (r - 1) d & r & 1 \end{array}| \end{array}$
where $a = \log A, d = \log R$
Use $C_{1} \to C_{1} - (a - d) C_{3} - d C_{3}$ to show $∆ = 0$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App