Sequence And Series Question 527
Question: $ 99^{th} $ term of the series $ 2+7+14+23+34+….. $ is
[Pb. CET 2003]
Options:
A) 9998
B) 9999
C) 10000
D) 100000
Show Answer
Answer:
Correct Answer: A
Solution:
Let $ S=2+7+14+23+34+…..+T_{n} $ ?..(i) and $ S=2+7+14+……………..+{T_{n-1}}+T_{n} $ ?..(ii) From (i) and (ii), we get $ 0=2+[5+7+9+11……..+T_{n}-{T_{n-1}}]-T_{n} $
$ \Rightarrow $ $ T_{n}=2+[ \frac{n-1}{2}{2\times 5+(n-2),2} ] $
$ \Rightarrow $ $ T_{n}=2+(n-1)(n+3) $ Now put $ n=99 $
$ \Rightarrow $ $ T_{99}=2+98\times 102=9998 $ .
BETA
