VITEEE 2009 Paper

Let a and R be the first term and common ratio of a Gp respectively.
So, Tp=aRp−1=x
Tq=aRq−1=y and Tr=aRr−1=z
⇒ log x = log a + (p - 1) log R
log y = log a + (q - 1) log R
and log z = log a + (r - 1) log R
∴|

log‌x	p	1
log‌y	q	1
log‌z	r	1

|=|

log‌a+(p−1)‌logR	p	1
log‌a+(q−1)‌logR	q	1
log‌a+(r−1)‌logR	r	1

|
=|

log‌a	p	1
log‌a	q	1
log‌a	r	1

|+|

(p−1)‌logR	p	1
(q−1)‌logR	q	1
(r−1)‌logR	r	1

|
= log a |

1	p	1
1	q	1
1	r	1

|+logR|

p−1	p−1	1
q−1	q−1	1
r−1	r−1	1

|(C2→C2−C3)
= 0 + 0 = 0 (∵ two columns are identical)