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

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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