Sequence And Series Question 445
Question: If the $ p^{th} $ term of an A.P. be $ q $ and $ q^{th} $ term be p, then its $ r^{th} $ term will be
[RPET 1999]
Options:
A) $ p+q+r $
B) $ p+q-r $
C) $ p+r-q $
D) $ p-q-r $
Show Answer
Answer:
Correct Answer: B
Solution:
Given that, $ T_{p}=a+(p-1)d=q $ ?..(i) and $ T_{q}=a+(q-1)d=p $ ?.. (ii) From (i) and (ii), we get $ d=-\frac{(p-q)}{(p-q)}=-1 $ Putting value of $ d $ in equation (i), then $ a=p+q-1 $ Now, $ r^{th} $ term is given by A.P. $ T_{r}=a+(r-1)d=(p+q-1)+(r-1)(-1) $ $ =p+q-r $ Note: Students should remember this question as a formula.
BETA
