logo

Ask Questions, Get Answers

 
X
 Search
Want to ask us a question? Click here
Browse Questions
Ad
Home  >>  CBSE XI  >>  Math  >>  Sequences and Series
0 votes

If the sum of $n$ terms of an $A.P.$ is $3n^2+5n$ and its $m^{th}$ term is $164$, find the value of $m$.

$\begin{array}{1 1}25 \\ 26 \\ 27 \\ 28 \end{array} $

Can you answer this question?
 
 

1 Answer

0 votes
Toolbox:
  • $S_n=\large\frac{n}{2}$$[2a+(n-1)d]$
  • In any series $S_n-S_{n-1}=t_n$
Given: sum of $n$ terms $S_n=3n^2+5n$
$\Rightarrow\:S_{n-1}=3(n-1)^2+5(n-1)$
We know that in any series $S_n-S_{n-1}=t_n$
$\Rightarrow\:t_n=\big[3n^2+5n\big]-\big[3(n-1)^2+5(n-1)\big]$
$\Rightarrow\:t_n=\big[3n^2+5n\big]-\big[3n^2-6n+3+5n-5\big]$
$\Rightarrow\:t_n=6n+2$
Also given that $m^{th}\:term=164$
$\Rightarrow\:t_m=164=6m+2$
$\Rightarrow\:m=27$
answered Feb 23, 2014 by rvidyagovindarajan_1
 

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
...