Which of the following sequences are in G.P.? (i) 3, 9, 27, 81,…

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

(i) 3, 9, 27, 81,…

Solution :

First term (a)  = 3, common ratio

r  = t2/t1   =  9/3 r = 3

r  = t3/t2   =  27/9 r = 3

r  = t2/t1   =  81/27 r = 3

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

5) Find the 17th term of the A.P 4 , 9 , 14 ,…………

Solution:

First term = 4

              a = 4

Common difference = 9 - 4  

                                 d = 5

n = 17

General term of an A.P

tn =  a + (n - 1) d

tn =  4 + (17 - 1) (5)

    = 4 + 16 (5)

    = 4 + 80

    = 84

Therefore 17th of A.P is 84