Which of the following sequences are in G.P.? (v) 1, −5, 25, −125,…

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

(v)  1, −5, 25, −125,…

Solution :

First term (a)  = 1/3, common ratio

r  = t2/t1   =  -5/1 r  = -5

r  = t2/t1   =  25/(-5) r = -5

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

Check whether the following sequences are in A.P. (iii) 9, 13, 17, 21, 25,...

Check whether the following sequences are in A.P.

(iii) 9, 13, 17, 21, 25,...

Solution :

d = t2 - t1 d = 13 - 9 d  = 4

d = t3 - t2 d = 17 - 13 d  = 4

The given sequence is an arithmetic progression.