Answer:
Given A.P. is 6, 13, 20, ???, 216 Here, \[~a=6,\text{ }d=13-6=20-13=7\] Let n be the number of terms. then \[{{T}_{n}}=a+(n-1)d\] \[216=6+(n-1)7\] \[216=6+7n-7\] \[217=7n\] \[\therefore n=31\] and middle term is \[\frac{(n+1)th}{2}\] term i.e., 16th term \[\therefore {{T}_{16}}=6+(16-1)7\] \[=6+15\times 7\] \[\therefore {{T}_{16}}=111\] \[\therefore \] Middle term of the A.P. is 111.
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