logo

Ask Questions, Get Answers

 
X
 Search
Want to ask us a question? Click here
Browse Questions
Ad
Home  >>  JEEMAIN and AIPMT  >>  Mathematics  >>  Class11  >>  Sequence and Series
0 votes

If the sum of first n terms of an AP is half the sum of next n terms, then $\large\frac{S_{4n}}{S_{n}}$ equals

$(a)\;10\qquad(b)\;8\qquad(c)\;6\qquad(d)\;4$

Can you answer this question?
 
 

1 Answer

0 votes
Answer : (a) 10
Explanation : Given ,
$S_{2n}-S_{n}=2S_{n}$
$S_{2n}=3S_{n}$
$\large\frac{2n}{2}\;[2a+(n-1)d]=\large\frac{3n}{2}\;[2a+(n-1)d]$
$4a+4nd-2d=6a+3nd-3d$
$2a=nd+d=(n-1)d$
$\large\frac{S_{4n}}{S_{n}}=\large\frac{\large\frac{4n}{2}\;[2a+(4n-1)d]}{\large\frac{n}{2}\;[2a+(n-1)d]}$
$\large\frac{S_{4n}}{S_{n}}=\large\frac{4\;[(n+1)d+(4n-1)d]}{[(n+1)d+(n-1)d]}$
$\large\frac{S_{4n}}{S_{n}}=\large\frac{4(5n)}{(2n)}=10\;.$
answered Jan 23, 2014 by yamini.v
 

Related questions

Ask Question
student study plans
x
JEE MAIN, CBSE, NEET Mobile and Tablet App
The ultimate mobile app to help you crack your examinations
Get the Android App
...