Question

Find out which of the following sequences are arithmetic progressions. For those which are arithmetic progressions, find out the common difference. $0,-4,-8,-12,....$

Answer 1

Given sequence is,

$0,-4,-8,-12,...\dots$

first term of this A.P is $a_1=0$

second term of this A.P is $a_2=-4$

third term of this A.P is $a_3=-8$

fourth term of this A.P is $a_4=-12$

the condition for an sequence to be an A.P is their must be a common difference $(i.e.,d=a_{n+1}-a_n)$

putting n=1 in above equation

$d=a_2-a_1=-4-0=-4$

putting n=2 in above equation

$d=a_3-a_2=-8-(-4)=-4$

putting n=3 in above equation

$d=a_4-a_3=-12-(-8)=-4$

as we can see we get a common difference $d=-4$ for this sequence

hence this sequence form an A.P

with first term $a_1=0$ and

common difference $d=-4$