Which of the following sequences are in G.P.? (vii) 16, 4, 1, 1/4,..........

Which of the following sequences are in G.P.?

(vii)  16, 4, 1, 1/4,..........

Solution :

First term (a)  = 16, common ratio

r  = t2/t1   =  4/16 r  = 1/4

r  = t2/t1  r  = 1/4

Since the common ratios are same, it is geometric sequence.

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.