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in Arithmetic Progression by (29.9k points)
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Find the middle term of the AP 6, 13, 20, …., 216.

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The given AP is 6,13,20,........,216.

First term, a = 6

Common difference, d = 13 - 6 = 7

Suppose these are n terms in the given AP. Then,

an = 216

Thus, the given AP contains 31 terms,

∴ Middle term of the given AP

\((\frac{31\,+\,1}{2})th\) term

= 16th term

= 6 + (16 - 1) x 7

= 6 + 105

= 111

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

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