Given AP is 6, 13, 20, … ,216.
The first and second terms of given AP are a1 = 6, a2 = 13 respectively.
The common difference of AP is d = a2 − a1 = 13 − 6 = 7.
The last term or nth term of AP is an = 216.
We know that nth term of AP is given by an = a1 + (n - 1)d.
We know that if n is odd then the middle term is \(\frac{n+1}{2}\)th term.
Thus, 16th term of given AP is middle term.
Therefore, the middle term of given AP is 16th term of given AP = a1 + 15d = 6 + 15 × 7
= 6 + 105 = 111.
Hence, the middle term of the AP 6, 13, 20, … , 216 is 111.
