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. the sum of $n$ terms is $5n^2−5n$. Find the $10^{th}$ term of the A.P.
Given: In an A.P. the sum of $n$ terms is $5n^2-5n$.
To do: To find the $10^{th}$ term of the A.P.
Solution:
Sum of the $n$ terms $=5n^2-5n$
$\because S_n=\frac{n}{2}( 2a+( n-1)d)$, where $a$ is the first term.
$S_1=$ Sum of $1$ term $=5-5=0$
$\therefore a_1=0\ .......(1)$
$S_2=$ Sum of $2$ terms $=5( 2)^2-5( 2)=10$
$\therefore a_1+a_2=10......( 2)$
Solving $( 1)$ and $( 2)$
$a_2=10$
$\therefore a_2=10$
$a_n=a+(n-1)d$
$\therefore a_1+d=10$
$\Rightarrow 0+d=10$
$\Rightarrow d=10$
$\therefore a_{10}=a+9d$
$=0+9(10)=90$
$\therefore a_{10}=90$
Thus, $10^{th}$ term of the A.P. is $90$.
Updated on: 10-Oct-2022
204 Views
Advertisements