The nth term of an A.P is 7-4n. Find its common difference.

Dear student,

1st term=7-4=3

2nd term=7-8=-1

Common difference=-4

T_n = a+(n-1)d

T_n = a-d + nd      ............1

T_n = 7 - 4n               (given)      .............2

comparing both

-4n = nd

d = -4

Put n=1 to obtain the first term,

a= 7-4 = 3.

Put n=2 to obtqin the second term,

a+d= 7-8 = -1.

Now d= (a+d)-d = -1 - 3 = -4.

common difference = -4