Find the common difference and write the next four terms of each of the following arithmetic progressions :$-1, \frac{1}{4}, \frac{3}{2}, ……..$

Given:

Given A.P. is $-1, \frac{1}{4}, \frac{3}{2}, ……..$.
To do:

We have to find the common difference and write the next four terms of the given A.P.
Solution:
 The common difference of an A.P. is the difference between any two consecutive terms.

Here,

$a_1=-1, a_2=\frac{1}{4}, a_3=\frac{3}{2}$

$d=a_2-a_1=\frac{1}{4}-(-1)=\frac{1}{4}+1=\frac{1+1\times4}{4}=\frac{5}{4}$

$a_4=a_3+d=\frac{3}{2}+\frac{5}{4}=\frac{3\times2+5}{4}=\frac{6+5}{4}=\frac{11}{4}$

$a_5=a_4+d=\frac{11}{4}+\frac{5}{4}=\frac{11+5}{4}=\frac{16}{4}=4$

$a_6=a_5+d=4+\frac{5}{4}=\frac{4\times4+5}{4}=\frac{16+5}{4}=\frac{21}{4}$

$a_7=a_6+d=\frac{21}{4}+\frac{5}{4}=\frac{21+5}{4}=\frac{26}{4}=\frac{13}{2}$

The common difference of the given A.P. is $\frac{5}{4}$ and the next four terms are $\frac{11}{4}, 4, \frac{21}{4}$ and $\frac{13}{2}$.  

Tutorialspoint

Simply Easy Learning

Updated on: 10-Oct-2022

34 Views

Kickstart Your Career

Get certified by completing the course

Get Started