Check whether the following sequences are in A.P. (iv) -1/3, 0, 1/3, 2/3.........

Check whether the following sequences are in A.P.

(iv) -1/3, 0, 1/3, 2/3.........

Solution :

d = t2 - t1 d = 0 - (-1/3) d  = 1/3

d = t3 - t2 d = (1/3) - 0 d  = 1/3

The given sequence is an arithmetic progression.

Check whether the following sequences are in A.P. (ii) 1/2, 1/3, 1/4, 1/5........

Check whether the following sequences are in A.P.

(ii)  1/2, 1/3, 1/4, 1/5........

Solution :

d = t2 - t1 d = (1/3) - (1/2)   =  (2 - 3)/6 d  = -1/6

d = t3 - t2 d = (1/4) - (1/3)   =  (3 - 4)/12 d  = -1/12

The common differences are not equal. Hence the given sequence is not A.P.