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Find the middle term of the A.P. 6, 13, 20, ... , 216.

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#### Solution

The given arithmetic progression is 6, 13, 20, ..., 216

Let 216 be the *n*^{th }term of the given AP.

So,

*a* = 6

*d* = 7

*a _{n} *= 216

Now,

a_{n}=a+(n−1)d

⇒216=6+(n−1)×7

⇒7(n−1)=210

⇒n−1 = `210/7`= 30

⇒n=31, which is odd

∴ Middle term of the AP

`=((31+1)/2)th` term of the AP

= 16th term of the AP

∴a_{16}=6+(16−1)×7=6+15×7=6+105=111

Thus, the middle term of the given AP is 111.

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