Sequence And Series Question 170
Question: The sums of terms of two arithmatic series are in the ratio $ 2n+3:6n+5 $ , then the ratio of their $ 13^{th} $ terms is
[MP PET 2004]
Options:
A) 53 : 155
B) 27 : 77
C) 29 : 83
D) 31 : 89
Show Answer
Answer:
Correct Answer: A
Solution:
We have $ \frac{{S_{n_1}}}{{S_{n_2}}}=\frac{2n+3}{6n+5} $
Þ $ \frac{\frac{n}{2}[2a_1+(n-1)d_1]}{\frac{n}{2}[2a_2+(n-1)d_2]}=\frac{2n+3}{6n+5} $
Þ $ \frac{2[ a_1+( \frac{n-1}{2} ),d_1 ]}{2[ a_2+( \frac{n-1}{2} ),d_2 ]}=\frac{2n+3}{6n+5} $
Þ $ \frac{a_1+( \frac{n-1}{2} ),d_1}{a_2+( \frac{n-1}{2} ),d_2}=\frac{2n+3}{6n+5} $ Put $ n=25 $ then $ \frac{a_1+12d_1}{a_2+12d_2}=\frac{2(25)+3}{6(25)+3} $
Þ $ \frac{{T_{13_1}}}{{T_{13_2}}}=\frac{53}{155} $ .
BETA
