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.

Find the middle term(s) of an A.P. 9, 15, 21, 27,…,183.

Find the middle term(s) of an A.P. 9, 15, 21, 27,…,183.

Solution :

In order to find the middle term of the sequence, first we have to know how many terms are in the given sequence.

n = [(l - a)d] + 1

a = 9, d = 15 - 9  ==> 6 and l = 183

n = [(183 - 9)/6] + 1

 n = (174 / 6) + 1

n = 29 + 1  = 30

n = 30(even)

middle terms are (n/2)th term and [(n/2) + 1]th term

15th term  = a + 14d =  9 + 14(6) =  93

16th term  = a + 15d =  9 + 15(6) =  99