Sequence And Series Question 296
Question: The common difference of an A.P. whose first term is unity and whose second, tenth and thirty fourth terms are in G.P., is
[AMU 2000]
Options:
A) $ \frac{1}{5} $
B) $ \frac{1}{3} $
C) $ \frac{1}{6} $
D) $ \frac{1}{9} $
Show Answer
Answer:
Correct Answer: B
Solution:
First term of an A.P. = 1, let Common difference = d
$ \therefore T_2=a+d,T_{10}=a+9d,T_{34}=a+33d $
$ \therefore {{(a+9d)}^{2}}=(a+d)(a+33d) $
Þ $ a^{2}+81d^{2}+18ad=a^{2}+ad+33ad+33d^{2} $ Put $ a=1 $
$ \Rightarrow 1+81d^{2}+18d=1+d+33d+33d^{2} $
Þ $ 48d^{2}-16d=0 $
$ \Rightarrow 16d(3d-1)=0 $
Þ $ d=0,d=1/3 $ .
BETA
