Find the common difference and write the next four terms of each of the following arithmetic progressions :$-1, -\frac{5}{6}, -\frac{2}{3}, ………..$

Given:

Given A.P. is $-1, -\frac{5}{6}, -\frac{2}{3}, ………..$.
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,

$a_1=-1, a_2=-\frac{5}{6}, a_3=-\frac{2}{3}$

$d=a_2-a_1=-\frac{5}{6}-(-1)=-\frac{5}{6}+1=\frac{-5+1\times6}{6}=\frac{1}{6}$

$a_4=a_3+d=-\frac{2}{3}+\frac{1}{6}=\frac{-2\times2+1}{6}=\frac{-4+1}{6}=\frac{-3}{6}=-\frac{1}{2}$

$a_5=a_4+d=\frac{-3}{6}+\frac{1}{6}=\frac{-3+1}{6}=\frac{-2}{6}=-\frac{1}{3}$

$a_6=a_5+d=\frac{-2}{6}+\frac{1}{6}=\frac{-2+1}{6}=\frac{-1}{6}$

$a_7=a_6+d=\frac{-1}{6}+\frac{1}{6}=\frac{-1+1}{6}=0$

The common difference of the given A.P. is $\frac{1}{6}$ and the next four terms are $-\frac{1}{2}, -\frac{1}{3}, -\frac{1}{6}$ and $0$.   

Tutorialspoint

e

Updated on: 10-Oct-2022

32 Views

Kickstart Your Career

Get certified by completing the course

Get Started