- Trending Categories
- 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