Check whether the following sequences are in A.P. (v) 1, -1, 1, -1, 1, -1,............

Check whether the following sequences are in A.P.

(v) 1, -1, 1, -1, 1, -1,............

Solution :

d = t2 - t1 d = -1 - 1 d  = -2

d = t3 - t2 d = 1 - (-1) =  1 + 1   =  2

The given sequence is not arithmetic progression.

Find the nth term of the following sequences (ii) 0, 1/2, 2/3, ............

Find the nth term of the following sequences

(ii) 0, 1/2, 2/3, ............

Solution :

Denominator is 1 more than the numerator. By approaching the above problem in this way, we will not get the first term.

Numerator is 1 less than the denominator.

  =  0, 1/2, 2/3, ............

  =  (1-1)/1, (2-1)/2, (3-1)/3, ...................

nth term of the sequence is (n - 1)/n

Find the nth term of the following sequences