find the 6th term from the end of the AP 5,2, -1 , -4................. -31 .

AP: 5, 2, -1, -4, ........, -31.

New AP: -31, -28, -25, -22, ..........., -4, -1, 2, 5.

a=-31 d=3 an=5

a₆=a+5d

=-31+5(3)

=-31+15

= -16

Therefore, The sixth term is -16.

n=6

a=5

d= -3

l = -31

TO FIND THE nTH TERM FROM THE LAST,

APPLY THE FORMULA - l - (n-1) d (where " l" =last term).

THEN WE WILL GET -= -31 - (6-1) * -3

= -31- (5)* -3

= -31 - -15

= -16 IS THE 6th TERM FROM THE END OF THIS A.P

SO FRIEND, DON'T FORGET TO GIVE A THUMBS UP......................

AP: 5, 2, -1, -4, ........, -31.

New AP: -31, -28, -25, -22, ..........., -4, -1, 2, 5.

a=-31 d=3 an=5

a₆=a+5d

=-31+5(3)

=-31+15

= -16

Therefore, The sixth term is -16.

OR it can be also solved as

n=6

a=5

d= -3

l = -31

TO FIND THE nTH TERM FROM THE LAST,

APPLY THE FORMULA -l - (n-1) d(where "l" =last term).

THEN WE WILL GET -=-31 - (6-1) * -3

= -31- (5)* -3

= -31--15

=-16IS THE 6th TERM FROM THE END OF THIS A.P