Sequence And Series Question 78
Question: If the $ p^{th},\ q^{th} $ and $ r^{th} $ term of an arithmetic sequence are a , b and $ c $ respectively, then the value of $
[a(q-r) $ + $ b(r-p) $ $ +c(p-q)]= $ [MP PET 1985]
Options:
A) 1
B) $ -1 $
C) 0
D) 1/2
Show Answer
Answer:
Correct Answer: C
Solution:
Suppose that first term and common difference of A.P.’s are $ A $ and D respectively. Now, $ p^{th} $ term $ =A+(p-1)D=a $ ?..(i) $ q^{th} $ term $ =A+(q-1)D=b $ ……(ii) and $ r^{th} $ term $ =A+(r-1)D=c $ ?..(iii) So, $ a(q-r)+b(r-p)+c(p-q) $ $ =a{ \frac{b-c}{D} }+b{ \frac{c-a}{D} }+c{ \frac{a-b}{D} } $ $ =\frac{1}{D}(ab-ac+bc-ab+ca-bc)=0 $ .
BETA
