![Trending Articles on Technical and Non Technical topics](/images/trending_categories.jpeg)
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
Find the 31st term of an AP whose 11th term is 38 and the 16th term is 73.
Given:
The 11th term of an AP is 38 and the 16th term is 73.
To do:
We have to find the 31st term of this AP.
Solution:
Let the first term of the A.P. be $a$ and the common difference be $d$.
We know that,
nth term of an A.P. $a_n=a+(n-1)d$
Therefore,
$a_{11}=a+(11-1)d=38$
$a+10d=38$.......(i)
$a_{16}=a+(16-1)d=73$
$a+15d=73$.......(ii)
Subtracting (i) from (ii), we get,
$a+15d-a-10d=73-38$
$5d=35$
$d=\frac{35}{5}$
$d=7$
This implies,
$a+10d=38$
$a+10(7)=38$
$a=38-70$
$a=-32$
Therefore,
$a_{31}=a+(31-1)d$
$=a+30d$
$=-32+30(7)$
$=210-32$
$=178$
The 31st term of the AP is $178$.
Advertisements