Answer:
Given A.P. is 213, 205, 197, .........., 37 Here Let n be the number of terms Then, \[{{T}_{n}}=a+(n-1)d\] \[37=213+(n-1)(-8)\] \[37=213-8n+8\] \[8n=184\] \[n=23\] And middle term is \[\frac{{{(n+1)}^{th}}}{2}\] term i.e. 12th term \[\therefore {{T}_{12}}=213+(12-1)(-8)\] \[=213+11(-8)\] \[=213-88\] \[\therefore {{T}_{12}}=125\] \[\therefore \] Middle term of the A.P. is \[125\].
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