Q. 174.7( 17 Votes )

Find the middle term of the AP 6, 13, 20, ..., 216.

Answer :

First term of the AP = 6

Common difference = d = 13 - 6 = 7


Last term = 216


Since


an = a + (n - 1) × d


216 = 6 + (n - 1) × 7


216 - 6 = 7n - 7


210 = 7n - 7


210 + 7 = 7n


7n = 217


n = 217/7 = 31


Middle term is (31 + 1)/2 = 16th


So, a16 = a + (16 - 1) × d


a16 = 6 + 15 × 7


a16 = 6 + 105 = 111


Middle term of the AP is 111.


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