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

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