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

a_{6}=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 "

*" =last term).*

**l**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

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