Question

write next three terms of the given ap (a+b) , (a+1) + b, (b+ 1)

Answer 1

Ap series :- any series is in AP when common difference is always constant
here given series ,
(a+b), (a+1)+b, (b+1) are in AP
only when
(a+1)+b-(a+b)=(b+1)-(a+1)-b
1=a
a=1
hence common difference =1=a
hence term
(a+b) +3a=4a+b or 4+b
(a+b)+4a=5a+b or 5+b
(a+b)+5a=6a+b or 6 +b

Answer 2

Given A.P ;
(a+b) , (a+1+b) , (b+1)

a = (a+b)
d = (a+1+b)-(a+b)
d = a+1+b-a-b
d = 1

d = (b+1)-(a+1+b)
1 = b+1-a-1-b
1 = -a
a = -1

The A.P with a=-1 & d=1 will be
-1,0,1,2,3,4,5,6....