- Data Structure
- Networking
- RDBMS
- Operating System
- Java
- MS Excel
- iOS
- HTML
- CSS
- Android
- Python
- C Programming
- C++
- C#
- MongoDB
- MySQL
- Javascript
- PHP
- Physics
- Chemistry
- Biology
- Mathematics
- English
- Economics
- Psychology
- Social Studies
- Fashion Studies
- Legal Studies
- Selected Reading
- UPSC IAS Exams Notes
- Developer's Best Practices
- Questions and Answers
- Effective Resume Writing
- HR Interview Questions
- Computer Glossary
- Who is Who
In an A.P. if $a = 1,\ a_n = 20$ and $S_n=399$, then find $n$.
Given: In an A.P. if $a = 1,\ a_n = 20$ and $S_n=399$.
To do: To find the value of $n$.
Solution:
Here, $a = 1,\ a_n = 20$ and $S_n=399$
Let $d$ be the common difference of the A.P.
As known,
$a_n=a+( n-1)d$
$\Rightarrow 20=1+( n-1)d$
$\Rightarrow ( n-1)d=20-1=19\ .........\ ( i)$
Sum of the $n$ terms of the A.P., $S_n=\frac{n}{2}[2a+( n-1)d]$
$\Rightarrow 399=\frac{n}{2}[2\times1+19]$
$\Rightarrow 399=\frac{n}{2}[21]$
$\Rightarrow n=\frac{399\times2}{21}$
$\Rightarrow n=38$
Thus, $n=38$.
Advertisements
To Continue Learning Please Login
Login with Google