Sequence And Series Question 380
Question: If the sum of the series $ 2+5+8+11………… $ is 60100, then the number of terms are
[MNR 1991; DCE 2001]
Options:
A) 100
B) 200
C) 150
D) 250
Show Answer
Answer:
Correct Answer: B
Solution:
Series,
$ \Rightarrow $ $ a(1-r)=12r $ and let number of terms is $ n $ then sum of A.P. $ a_1+a_5+a_{10}+a_{15}+a_{20}+a_{24}=225 $
$ \Rightarrow $ $ 60100=\frac{n}{2}{ 2\times 2+(n-1)3 } $
$ \Rightarrow $ $ 120200=n(3n+1) $
$ \Rightarrow $ $ 3n^{2}+n-120200=0 $
$ \Rightarrow $ $ (n-200)(3n+601)=0 $ Hence $ n=200 $ .
BETA
