Sequence And Series Question 374
Question: If a, b, and c are in A.P ., and p and p’ are, respectively, A.M. and G.M. between a and b while q, q’ are, respectively, the A,M. and G M. between b and c, then
Options:
A) $ p^{2}+q^{2}=p{{’}^{2}}+q{{’}^{2}} $
B) $ pq=p’q’ $
C) $ p^{2}-q^{2}=p{{’}^{2}}-q{{’}^{2}} $
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
[c] $ 2b=a+c; $ a, p, b, q, c, are in A.P. Hence $ p=\frac{a+b}{2} $ and $ q=\frac{b+c}{2} $ Again, a, p’, b, q’ and c = are in G.P. Hence, $ p’=\sqrt{ab} $ and $ q’=\sqrt{bc} $ $ p^{2}-q^{2}=\frac{(a-c)(a+c+2b)}{4} $ $ =\frac{(a-c)(2b+2b)}{4} $ $ [\because a+c=2b] $ $ =(a-c),b=ab-bc=p{{’}^{2}}-q{{’}^{2}} $
BETA
