- 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 $a,\ b$ and $c$ such that the following numbers are in A.P. $a,\ 7,\ b,\ 23,\ c$
Given: An A.P. $a,\ 7,\ b,\ 23,\ c$.
To do: To find $a,\ b$ and $c$.
Solution:
$a,\ 7,\ b,\ 23,\ c$ are in AP
Therefore, $7-a=d$ ......$( i)$
$b-7=d$ ....... $( ii)$
$23-b=d$ ....... $( iv)$
$c-23=d$ ....... $( v)$
From $( i)$ and ( ii)$
$7-a=b-7$
$\Rightarrow -b-a=-14$
$\Rightarrow a+b=14$ ....... $( vi)$
From $( ii)$ and $( iv)$
$b-7=23-b$
$\Rightarrow b+b=23+7$
$\Rightarrow 2b=30$
$\Rightarrow b=\frac{30}{2}$
$\Rightarrow b=15$, Put this in equation $( vi)$
$a+15=14$
$\Rightarrow a=14-15=-1$
Now, from $( iv)$ and $( v)$
$c-23=23-b$
$\Rightarrow c-23=23-15$
$\Rightarrow c-23=8$
$\Rightarrow c=8+23$
$\Rightarrow c=31$
Thus, the values of $a,\ b$ and $c$ are $-1,\ 15$ and $31$ respectively.
Advertisements