Sequence And Series Question 154
Question: If $ p $ times the $ p^{th} $ term of an A.P. is equal to $ q $ times the $ q^{th} $ term of an A.P., then $ {{(p+q)}^{th}} $ term is
[MP PET 1997; Karnataka CET 2002]
Options:
A) 0
B) 1
C) 2
D) 3
Show Answer
Answer:
Correct Answer: A
Solution:
$ p{a+(p-1),d}=q{a+(q-1),d} $
$ \Rightarrow $ $ a(p-q)+(p^{2}-q^{2}),d+(q-p),d=0 $
$ \Rightarrow $ $ (p-q){a+(p+q-1),d}=0 $
$ \Rightarrow $ $ a+(p+q-1),d=0 $
$ \Rightarrow $ $ {T_{p+q}}=0 $ , $ {\because \ p\ne q} $ .
BETA
